###### Monte Carlo Method

In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)

###### Markov Chains

###### Computer Simulation

###### Bayes Theorem

A theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihood of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result.

###### Radiometry

###### Algorithms

###### Models, Statistical

###### Photons

###### Phantoms, Imaging

Devices or objects in various imaging techniques used to visualize or enhance visualization by simulating conditions encountered in the procedure. Phantoms are used very often in procedures employing or measuring x-irradiation or radioactive material to evaluate performance. Phantoms often have properties similar to human tissue. Water demonstrates absorbing properties similar to normal tissue, hence water-filled phantoms are used to map radiation levels. Phantoms are used also as teaching aids to simulate real conditions with x-ray or ultrasonic machines. (From Iturralde, Dictionary and Handbook of Nuclear Medicine and Clinical Imaging, 1990)

###### Radiotherapy Planning, Computer-Assisted

###### Models, Genetic

###### Models, Biological

###### Scattering, Radiation

###### Likelihood Functions

###### Models, Theoretical

###### Software

###### Models, Chemical

###### Stochastic Processes

###### Reproducibility of Results

The statistical reproducibility of measurements (often in a clinical context), including the testing of instrumentation or techniques to obtain reproducible results. The concept includes reproducibility of physiological measurements, which may be used to develop rules to assess probability or prognosis, or response to a stimulus; reproducibility of occurrence of a condition; and reproducibility of experimental results.

###### Thermodynamics

A rigorously mathematical analysis of energy relationships (heat, work, temperature, and equilibrium). It describes systems whose states are determined by thermal parameters, such as temperature, in addition to mechanical and electromagnetic parameters. (From Hawley's Condensed Chemical Dictionary, 12th ed)

###### Models, Molecular

###### Protein Conformation

The characteristic 3-dimensional shape of a protein, including the secondary, supersecondary (motifs), tertiary (domains) and quaternary structure of the peptide chain. PROTEIN STRUCTURE, QUATERNARY describes the conformation assumed by multimeric proteins (aggregates of more than one polypeptide chain).

###### Radiation Dosage

The amount of radiation energy that is deposited in a unit mass of material, such as tissues of plants or animal. In RADIOTHERAPY, radiation dosage is expressed in gray units (Gy). In RADIOLOGIC HEALTH, the dosage is expressed by the product of absorbed dose (Gy) and quality factor (a function of linear energy transfer), and is called radiation dose equivalent in sievert units (Sv).

###### Genetic Markers

###### Evolution, Molecular

###### Chromosome Mapping

###### Entomology

###### Arthropods

## Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries. (1/4146)

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model. (+info)## Temporal and multiple quantitative trait loci analyses of resistance to bacterial wilt in tomato permit the resolution of linked loci. (2/4146)

Ralstonia solanacearum is a soil-borne bacterium that causes the serious disease known as bacterial wilt in many plant species. In tomato, several QTL controlling resistance have been found, but in different studies, markers spanning a large region of chromosome 6 showed strong association with the resistance. By using two different approaches to analyze the data from a field test F3 population, we show that at least two separate loci approximately 30 cM apart on this chromosome are most likely involved in the resistance. First, a temporal analysis of the progression of symptoms reveals a distal locus early in the development of the disease. As the disease progresses, the maximum LOD peak observed shifts toward the proximal end of the chromosome, obscuring the distal locus. Second, although classical interval mapping could only detect the presence of one locus, a statistical "two-QTL model" test, specifically adapted for the resolution of linked QTL, strongly supported the hypothesis for the presence of two loci. These results are discussed in the context of current molecular knowledge about disease resistance genes on chromosome 6 and observations made by tomato breeders during the production of bacterial wilt-resistant varieties. (+info)## Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors. (3/4146)

In cardiac muscle, release of activator calcium from the sarcoplasmic reticulum occurs by calcium- induced calcium release through ryanodine receptors (RyRs), which are clustered in a dense, regular, two-dimensional lattice array at the diad junction. We simulated numerically the stochastic dynamics of RyRs and L-type sarcolemmal calcium channels interacting via calcium nano-domains in the junctional cleft. Four putative RyR gating schemes based on single-channel measurements in lipid bilayers all failed to give stable excitation-contraction coupling, due either to insufficiently strong inactivation to terminate locally regenerative calcium-induced calcium release or insufficient cooperativity to discriminate against RyR activation by background calcium. If the ryanodine receptor was represented, instead, by a phenomenological four-state gating scheme, with channel opening resulting from simultaneous binding of two Ca2+ ions, and either calcium-dependent or activation-linked inactivation, the simulations gave a good semiquantitative accounting for the macroscopic features of excitation-contraction coupling. It was possible to restore stability to a model based on a bilayer-derived gating scheme, by introducing allosteric interactions between nearest-neighbor RyRs so as to stabilize the inactivated state and produce cooperativity among calcium binding sites on different RyRs. Such allosteric coupling between RyRs may be a function of the foot process and lattice array, explaining their conservation during evolution. (+info)## Quantal amplitude and quantal variance of strontium-induced asynchronous EPSCs in rat dentate granule neurons. (4/4146)

1. Excitatory postsynaptic currents (EPSCs) were recorded from granule cells of the dentate gyrus in acute slices of 17- to 21-day-old rats (22-25 C) using tissue cuts and minimal extracellular stimulation to selectively activate a small number of synaptic contacts. 2. Adding millimolar Sr2+ to the external solution produced asynchronous EPSCs (aEPSCs) lasting for several hundred milliseconds after the stimulus. Minimally stimulated aEPSCs resembled miniature EPSCs (mEPSCs) recorded in the same cell but differed from them in ways expected from the greater range of dendritic filtering experienced by mEPSCs. aEPSCs had the same stimulus threshold as the synchronous EPSCs (sEPSCs) that followed the stimulus with a brief latency. aEPSCs following stimulation of distal inputs had a slower mean rise time than those following stimulation of proximal inputs. These results suggest that aEPSCs arose from the same synapses that generated sEPSCs. 3. Proximally elicited aEPSCs had a mean amplitude of 6.7 +/- 2.2 pA (+/- s.d., n = 23 cells) at -70 mV and an amplitude coefficient of variation of 0. 46 +/- 0.08. 4. The amplitude distributions of sEPSCs never exhibited distinct peaks. 5. Monte Carlo modelling of the shapes of aEPSC amplitude distributions indicated that our data were best explained by an intrasite model of quantal variance. 6. It is concluded that Sr2+-evoked aEPSCs are uniquantal events arising at synaptic terminals that were recently invaded by an action potential, and so provide direct information about the quantal amplitude and quantal variance at those terminals. The large quantal variance obscures quantization of the amplitudes of evoked sEPSCs at this class of excitatory synapse. (+info)## Bayesian inference on biopolymer models. (5/4146)

MOTIVATION: Most existing bioinformatics methods are limited to making point estimates of one variable, e.g. the optimal alignment, with fixed input values for all other variables, e.g. gap penalties and scoring matrices. While the requirement to specify parameters remains one of the more vexing issues in bioinformatics, it is a reflection of a larger issue: the need to broaden the view on statistical inference in bioinformatics. RESULTS: The assignment of probabilities for all possible values of all unknown variables in a problem in the form of a posterior distribution is the goal of Bayesian inference. Here we show how this goal can be achieved for most bioinformatics methods that use dynamic programming. Specifically, a tutorial style description of a Bayesian inference procedure for segmentation of a sequence based on the heterogeneity in its composition is given. In addition, full Bayesian inference algorithms for sequence alignment are described. AVAILABILITY: Software and a set of transparencies for a tutorial describing these ideas are available at http://www.wadsworth.org/res&res/bioinfo/ (+info)## A hierarchical approach to protein molecular evolution. (6/4146)

Biological diversity has evolved despite the essentially infinite complexity of protein sequence space. We present a hierarchical approach to the efficient searching of this space and quantify the evolutionary potential of our approach with Monte Carlo simulations. These simulations demonstrate that nonhomologous juxtaposition of encoded structure is the rate-limiting step in the production of new tertiary protein folds. Nonhomologous "swapping" of low-energy secondary structures increased the binding constant of a simulated protein by approximately 10(7) relative to base substitution alone. Applications of our approach include the generation of new protein folds and modeling the molecular evolution of disease. (+info)## The topomer-sampling model of protein folding. (7/4146)

Clearly, a protein cannot sample all of its conformations (e.g., approximately 3(100) approximately 10(48) for a 100 residue protein) on an in vivo folding timescale (<1 s). To investigate how the conformational dynamics of a protein can accommodate subsecond folding time scales, we introduce the concept of the native topomer, which is the set of all structures similar to the native structure (obtainable from the native structure through local backbone coordinate transformations that do not disrupt the covalent bonding of the peptide backbone). We have developed a computational procedure for estimating the number of distinct topomers required to span all conformations (compact and semicompact) for a polypeptide of a given length. For 100 residues, we find approximately 3 x 10(7) distinct topomers. Based on the distance calculated between different topomers, we estimate that a 100-residue polypeptide diffusively samples one topomer every approximately 3 ns. Hence, a 100-residue protein can find its native topomer by random sampling in just approximately 100 ms. These results suggest that subsecond folding of modest-sized, single-domain proteins can be accomplished by a two-stage process of (i) topomer diffusion: random, diffusive sampling of the 3 x 10(7) distinct topomers to find the native topomer ( approximately 0.1 s), followed by (ii) intratopomer ordering: nonrandom, local conformational rearrangements within the native topomer to settle into the precise native state. (+info)## Testing the fit of a quantal model of neurotransmission. (8/4146)

Many studies of synaptic transmission have assumed a parametric model to estimate the mean quantal content and size or the effect upon them of manipulations such as the induction of long-term potentiation. Classical tests of fit usually assume that model parameters have been selected independently of the data. Therefore, their use is problematic after parameters have been estimated. We hypothesized that Monte Carlo (MC) simulations of a quantal model could provide a table of parameter-independent critical values with which to test the fit after parameter estimation, emulating Lilliefors's tests. However, when we tested this hypothesis within a conventional quantal model, the empirical distributions of two conventional goodness-of-fit statistics were affected by the values of the quantal parameters, falsifying the hypothesis. Notably, the tests' critical values increased when the combined variances of the noise and quantal-size distributions were reduced, increasing the distinctness of quantal peaks. Our results support two conclusions. First, tests that use a predetermined critical value to assess the fit of a quantal model after parameter estimation may operate at a differing unknown level of significance for each experiment. Second, a MC test enables a valid assessment of the fit of a quantal model after parameter estimation. (+info)###### Monte Carlo simulation of xenon adsorption with dealumination of an idealized mordenite structure<...

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###### Nicholas Metropolis

... developed the

**Monte****Carlo****method**.[5] Generally speaking, the**Monte****Carlo****method**is a statistical approach to solve ... team that came up with the name**Monte****Carlo****method**in reference to a colleague's relative's love for the casinos of**Monte****Carlo**...**Monte****Carlo****method**[edit]. At Los Alamos, in the 1950s, a group of researchers led by Metropolis, including John von Neumann and ...**Monte****Carlo****methods**are a class of computational algorithms that rely on repeated random sampling to compute their results. In ...###### Reinforcement learning

**Monte**

**Carlo**

**methods**[edit].

**Monte**

**Carlo**

**methods**can be used in an algorithm that mimics policy iteration. Policy iteration ...

**Monte**

**Carlo**. Every visit to

**Monte**

**Carlo**. Model-Free. Either. Discrete. Discrete. Sample-means ... that can continuously interpolate between

**Monte**

**Carlo**

**methods**that do not rely on the Bellman equations and the basic TD ... The two approaches available are gradient-based and gradient-free

**methods**. Gradient-based

**methods**(policy gradient

**methods**) ...

###### Energy-based generative neural network

Barbu, Adrian; Zhu, Song-Chun (2020).

**Monte****Carlo****Methods**. Springer. Wu, Ying Nian; Xie, Jianwen; Lu, Yang; Zhu, Song-Chun ( ... The parameter of the neural network in this model is trained in a generative manner by Markov chain**Monte****Carlo**(MCMC)-based ... the algorithm samples the synthesized examples from the current model by a gradient-based MCMC**method**, e.g., Langevin dynamics ...###### Simultaneous localization and mapping

**Monte**

**Carlo**

**methods**). They provide an estimation of the posterior probability function for the pose of the robot and for the ...

**Monte**

**Carlo**localization Multi Autonomous Ground-robotic International Challenge: A $1.6 million international challenge ... Typical loop closure

**methods**apply a second algorithm to compute some type of sensor measure similarity, and re-set the ...

**Methods**which conservatively approximate the above model using Covariance intersection are able to avoid reliance on ...

###### Low-discrepancy sequence

Discrepancy theory Markov chain

**Monte****Carlo**Quasi-**Monte****Carlo****method**Sparse grid BECK, A two-dimensional van Aardenne-Ehrenfest ... this is the**Monte****Carlo****method**. If the points are chosen as elements of a low-discrepancy sequence, this is the quasi-**Monte**... Elements need not be recomputed in the random**Monte****Carlo****method**if N is increased, but the point sets do not have minimal ... Hammersley, J. M.; Handscomb, D. C. (1964).**Monte****Carlo****Methods**. doi:10.1007/978-94-009-5819-7. Herman Tulleken. "Poisson Disk ...###### Stochastic programming

**Monte**

**Carlo**sampling and Sample Average Approximation (SAA)

**Method**[edit]. A common approach to reduce the scenario set to a ... or it can be generated by

**Monte**

**Carlo**sampling techniques. Then we can formulate a corresponding sample average approximation ... This formulation is known as the Sample Average Approximation

**method**. The SAA problem is a function of the considered sample ... manageable size is by using

**Monte**

**Carlo**simulation. Suppose the total number of scenarios is very large or even infinite. ...

###### Multicanonical ensemble

**Monte**

**Carlo**statistical

**methods**. Springer. ISBN 978-0-387-21239-5. Wolff, U. (1989). "Collective

**Monte**

**Carlo**Updating for Spin ... Generally,

**Monte**

**Carlo**

**methods**' idea is to use importance sampling to improve the convergence of the estimator Q ¯ N {\ ... Like in any other

**Monte**

**Carlo**

**method**, there are correlations of the samples being drawn from P ( r ) {\displaystyle P({\ ... Newmann, M E J; Barkema, G T (2002).

**Monte**

**Carlo**

**Methods**in Statistical Physics. USA: Oxford University Press. ISBN 0198517971 ...

###### Rejection sampling

In high dimensions, it is necessary to use a different approach, typically a Markov chain

**Monte****Carlo****method**such as Metropolis ... Robert, C.P. and Casella, G. "**Monte****Carlo**Statistical**Methods**" (second edition). New York: Springer-Verlag, 2004. J. von ...**Monte****Carlo****methods**", Nat. Bureau Standards, 12 (1951), pp. 36-38.. ... and is a type of exact simulation**method**. The**method**works for any distribution in R m {\displaystyle \mathbb {R} ^{m}} with a ...###### George Casella

His contributions focused on the area of statistics including

**Monte****Carlo****methods**, model selection, and genomic analysis. He ... ISBN 978-0-387-75965-4. Casella, George; Robert, Christian P. (2009). Introducing**Monte****Carlo****Methods**with R (Use R). Berlin: ... ISBN 0-534-24312-6. Casella, George; Robert, Christian P. (2004).**Monte****Carlo**statistical**methods**. Berlin: Springer. ISBN 0-387 ... on assessing and accelerating the convergence of Markov chain**Monte****Carlo****methods**, as in his Rao-Blackwellisation technique, ...###### FERMIAC

... and the

**MONTE****CARLO****METHOD**" (PDF). Los Alamos Science: 131. Metropolis, Nicholas; Ulam, S. (1949). "The**Monte****Carlo****Method**". ... He discussed his ideas with John von Neumann, who eventually used the ENIAC to implement the**Monte****Carlo****method**(as the ... The FERMIAC employed the**Monte****Carlo****method**to model neutron transport in various types of nuclear systems. Given an initial ... Metropolis, Nicholas (1987). "The Beginning of the**Monte****Carlo****Method**" (PDF). Los Alamos Science (15): 125. "The Fermiac or ...###### Timeline of computational mathematics

The

**Monte****Carlo****Method**: Classic Papers**Monte****Carlo**Landmark Papers. ... N. Metropolis and S. Ulam (1949). The**Monte****Carlo****method**. Journal of the American Statistical Association 44:335-341. "SIAM ... "The Beginning of the**Monte****Carlo****method**" (PDF). Los Alamos Science. No. 15, Page 125.. Accessed 5 may 2012. S. Ulam, R. D. ...**Monte****Carlo**simulation (voted one of the top 10 algorithms of the 20th century) invented at Los Alamos by von Neumann, Ulam and ...###### ENIAC

The success of this project showed the value of

**Monte****Carlo****methods**in science. A press conference was held on February 1, 1946 ... Related to ENIAC's role in the hydrogen bomb was its role in the**Monte****Carlo****method**becoming popular. Scientists involved in ... The**Monte****Carlo****Method**. Engineering Applications. ACMO Academic Press. p. 250. ISBN 978-619-90684-3-4. Kean, Sam (2010). The ... The "first production run" of the new coding techniques on the**Monte****Carlo**problem followed in April. After ENIAC's move to ...###### KISS (algorithm)

**Monte**

**Carlo**Statistical

**Methods**. Springer. pp. 39-43. ISBN 978-1-4757-3071-5. Rose, Gregory G. (2017). "KISS: A bit too simple ...

###### Song-Chun Zhu

A.Barbu and S.C. Zhu,

**Monte****Carlo****Methods**, Springer, Published in 2019. S.C. Zhu, AI: The Era of Big Integration - Unifying ... "**Monte****Carlo****Methods**(Hardback)". "A letter from the PAMI TC and CVPR 2019 organizers". "DMAI". "DMAI". Zhu, S. C., Wu, Y., & ... as a unified representation and numerous**Monte****Carlo****methods**for inference and learning. In 2005, Zhu established an ... Tu, Z. and Zhu, S.-C. Image Segmentation by Data Driven Markov Chain**Monte****Carlo**, IEEE Trans. on PAMI, 24(5), 657-673, 2002. Tu ...###### Timeline of scientific computing

Metropolis, N. (1987). "The Beginning of the

**Monte****Carlo****method**" (PDF). Los Alamos Science. No. 15, Page 125.. Accessed 5 may ... Metropolis, N.; Ulam, S. (1949). "The**Monte****Carlo****method**". Journal of the American Statistical Association. 44 (247): 335-341. ... that would later become the foundation of the**Monte****Carlo****method**. See also FERMIAC. Shannon explains how to use electric ... 1947 -**Monte****Carlo**simulation (voted one of the top 10 algorithms of the 20th century)[citation needed] invented at Los Alamos ...###### N-body units

Hénon, Michel (1971). "The

**Monte****Carlo****Method**". Astrophysics and Space Science. 14 (1): 151-167. Bibcode:1971Ap&SS..14..151H. ...###### Stanislaw Ulam

"The

**Monte****Carlo****method**". Metropolis and Ulam published the first unclassified paper on the**Monte****Carlo****method**in 1949. Fermi, ... The**Monte****Carlo****method**has become a ubiquitous and standard approach to computation, and the**method**has been applied to a vast ... Ulam, who was to become an originator of the**Monte****Carlo****method**and co-discoverer of the hydrogen-bomb,... used to tease me by ... The Day After Trinity at IMDb Eckhardt, Roger (1987). "Stan Ulam, John von Neumann, and the**Monte****Carlo****Method**" (PDF). Los ...###### Random number generation

Pseudorandom number generators are very useful in developing

**Monte****Carlo**-**method**simulations, as debugging is facilitated by the ... Handbook of**Monte****Carlo****Methods**. New York: John Wiley & Sons. p. 772. ISBN 978-0-470-17793-8. Press, WH; Teukolsky, SA; ... such as the computation of integrals by the**Monte****Carlo****method**. For such problems, it may be possible to find a more accurate ... One**method**, called the inversion**method**, involves integrating up to an area greater than or equal to the random number (which ...###### Cauchy process

Kroese, D.P.; Taimre, T.; Botev, Z.I. (2011). Handbook of

**Monte****Carlo****Methods**. John Wiley & Sons. p. 214. ISBN 9781118014950. ... Bertoin, J. (2001). "Some elements on Lévy processes". In Shanbhag, D.N. (ed.). Stochastic Processes: Theory and**Methods**. Gulf ...###### Antithetic variates

In statistics, the antithetic variates

**method**is a variance reduction technique used in**Monte****Carlo****methods**. Considering that ... Kroese, D. P.; Taimre, T.; Botev, Z. I. (2011). Handbook of**Monte****Carlo****methods**. John Wiley & Sons.(Chapter 9.3). ... using**Monte****Carlo****methods**) has a one-over square root convergence, a very large number of sample paths is required to obtain an ... The following table compares the classical**Monte****Carlo**estimate (sample size: 2n, where n = 1500) to the antithetic variates ...###### Quantile function

... as they work well with multivariate techniques based on either copula or quasi-

**Monte**-**Carlo****methods**and**Monte****Carlo****methods**in ... ISBN 1-58488-174-7. Jaeckel, P. (2002).**Monte****Carlo****methods**in finance. Steinbrecher, G., Shaw, W.T. (2008). "Quantile ... Quantile functions are used in both statistical applications and**Monte****Carlo****methods**. The quantile function is one way of ...**Monte**-**Carlo**simulations employ quantile functions to produce non-uniform random or pseudorandom numbers for use in diverse ...###### Computer simulation

see also:

**Monte****Carlo****method**). multiparticle simulation of the response of nanomaterials at multiple scales to an applied force ... Techniques used for such simulations are Molecular dynamics, Molecular mechanics,**Monte****Carlo****method**, and Multiscale Green's ... It was a simulation of 12 hard spheres using a**Monte****Carlo**algorithm. Computer simulation is often used as an adjunct to, or ... exploration program involves combining samples from a variety of statistical distributions using the**Monte****Carlo****method**. If, ...###### Undergraduate Texts in Mathematics

Explorations in

**Monte****Carlo****Methods**. doi:10.1007/978-0-387-87837-9. ISBN 978-0-387-87836-2. Stein, William (2009). Elementary ... doi:10.1007/978-1-4612-6153-7. ISBN 978-0-387-90357-6. Franklin, Joel (1980).**Methods**of Mathematical Economics: Linear and ...###### Path integral molecular dynamics

doi:10.1016/0370-1573(75)90030-7. Barker, J. A. (1979). "A quantum-statistical

**Monte****Carlo****method**; path integrals with boundary ...**method**. The same techniques are also used in path integral**Monte****Carlo**(PIMC). The technique has been used to calculate time ... John Shumway; Matthew Gilbert (2008). "Path Integral**Monte****Carlo**Simulation".CS1 maint: multiple names: authors list (link). ... Jang, S.; Voth, G. A. (1999). "A derivation of centroid molecular dynamics and other approximate time evolution**methods**for ...###### Nested sampling algorithm

Chen, Ming-Hui, Shao, Qi-Man, and Ibrahim, Joseph George (2000).

**Monte****Carlo****methods**in Bayesian computation. Springer. ISBN ... an efficient and robust alternative to Markov Chain**Monte****Carlo****methods**for astronomical data analyses". MNRAS. 384 (2): 449- ... Update the point with least likelihood with some Markov chain**Monte****Carlo**steps according to the prior, accepting only steps ... "Point-process based**Monte****Carlo**estimation". Statistics and Computing. 27: 219-236. arXiv:1412.6368. doi:10.1007/s11222-015- ...###### Pollard's rho algorithm

... for logarithms Pollard's kangaroo algorithm Pollard, J. M. (1975). "A

**Monte****Carlo****method**for ... "An Improved**Monte****Carlo**Factorization Algorithm". BIT. 20: 176-184. doi:10.1007/BF01933190. CS1 maint: discouraged parameter ( ... In that case, the**method**can be tried again, using a starting value other than 2 or a different g ( x ) {\displaystyle g(x)} . ... He used the same core ideas as Pollard but a different**method**of cycle detection, replacing Floyd's cycle-finding algorithm ...###### Ivan Dimov (scientist)

His research interests include

**Monte****Carlo**and quasi-**Monte****Carlo****methods**, superconvergent statistical numerical**methods**, ... Dimov, Ivan (2008).**Monte****Carlo****Methods**for Applied Scientists. New Jersey: World Scientific. ISBN 978-981-02-2329-8. CS1 maint ... He has published 3 monographs - Computational and Numerical Challenges in Environmental Modelling (2006),**Monte****Carlo****Methods**... Dimov has published over 150 articles in peer-reviewed international scientific journals, including Numerical**Methods**and ...###### Markov chain

Therefore, Markov Chain

**Monte****Carlo****method**can be used to draw samples randomly from a black-box to approximate the probability ... The use of Markov chains in Markov chain**Monte****Carlo****methods**covers cases where the process follows a continuous state space. ... Markov processes are the basis for general stochastic simulation**methods**known as Markov chain**Monte****Carlo**, which are used for ... Reuven Y. Rubinstein; Dirk P. Kroese (20 September 2011). Simulation and the**Monte****Carlo****Method**. John Wiley & Sons. p. 225. ...###### Stochastic process

For example, they are the basis for a general stochastic simulation

**method**known as Markov chain**Monte****Carlo**, which is used for ... ISBN 978-0-08-057041-9. Reuven Y. Rubinstein; Dirk P. Kroese (2011). Simulation and the**Monte****Carlo****Method**. John Wiley & Sons. ... ISBN 978-0-19-852525-7.**Carlo**Laing; Gabriel J Lord (2010). Stochastic**Methods**in Neuroscience. OUP Oxford. ISBN 978-0-19- ... ISBN 978-1-118-21052-9. Dani Gamerman; Hedibert F. Lopes (2006). Markov Chain**Monte****Carlo**: Stochastic Simulation for Bayesian ...###### Control variates

The control variates

**method**is a variance reduction technique used in**Monte****Carlo****methods**. It exploits information about the ... Glasserman, P. (2004).**Monte****Carlo****Methods**in Financial Engineering. New York: Springer. ISBN 0-387-00451-3 (p. 185) Botev, Z ... using**Monte****Carlo**integration. This integral is the expected value of f ( U ) {\displaystyle f(U)} , where f ( U ) = 1 1 + U {\ ... they can be estimated across the**Monte****Carlo**replicates. This is equivalent to solving a certain least squares system; ...###### Computational neuroscience

Stereochemically detailed models of the acetylcholine receptor-based synapse with the

**Monte****Carlo****method**, working at the time ... With the emergence of two-photon microscopy and calcium imaging, we now have powerful experimental**methods**with which to test ... There have been some attempts to provide unified**methods**that bridge and integrate these levels of complexity.[33] ...###### Super-Kamiokande

In the Super-Kamiokande detector, Rmean for uniformly distributed

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"Markov Chain

**Monte****Carlo**" para análise bayesiano de problemas baseados en modelos probabilísticos.[129] ... "**Methods**in Molecular Biology 226.. *↑ Burke, D. T., el al. (1987). "Cloning of Large Segments of Exogenous DNA into Yeast by ... Artificial Intelligence and Heuristic**Methods**in Bioinformatics. IOS Press. ISBN 1586032941.. *↑ Murray-Rust, P.; et al. (2005 ... Needleman, S. y Wunsch, C. (1970). "A general**method**applicable to the search for similarities in the amino acid sequence of ...###### Materials science

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###### Probability distribution

A frequent problem in statistical simulations (the

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**Carlo**Goldoni is known to have burned his first play, a tragedy called Amalasunta, when encountering unfavorable criticism. ... At the beginning of the Battle of

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Markov chain

**Monte****Carlo**. *. Mathematics portal. .mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw- ... Empirical Bayes**method**. *Cromwell's rule. *Bernstein-von Mises theorem. *Schwarz criterion. *Credible interval ...###### Mortgage-backed security

Practitioners typically use specialised

**Monte****Carlo****methods**or modified Binomial Tree numerical solutions. ... In models of this type, numerical**methods**provide approximate theoretical prices. These are also required in most models that ...###### Protein

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**Methods**of study. Main article: Protein

**methods**. The activities and structures of proteins may be examined in vitro, in vivo, ...

**Methods**in Molecular Biology (Clifton, N.j.).

**Methods**in Molecular Biology. 815. pp. 15-24. doi:10.1007/978-1-61779-424-7_2. ...

**Methods**in Molecular Biology.

**Methods**in Molecular Biology™. 424. pp. 225-39. doi:10.1007/978-1-60327-064-9_19. ISBN 978-1- ...

###### Mesa Verde National Park

Webb, Robert H.; Boyer, Diane E.; Turner, Raymond M. (2010), Repeat Photography:

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In addition there are Markov chain

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Moss, G. D.; Pasko, V. P.; Liu, N.; Veronis, G. (2006). "

**Monte****Carlo**model for analysis of thermal runaway electrons in ... Chu, P.K.; Lu, XinPel (2013). Low Temperature Plasma Technology:**Methods**and Applications. CRC Press. ISBN 978-1-4665-0990-0. . ... Chu, P.K.; Lu, XinPel (2013). Low Temperature Plasma Technology:**Methods**and Applications. CRC Press. p. 3. ISBN 978-1-4665- ... Magnetically induced plasmas (MIP), typically produced using microwaves as a resonant coupling**method**...###### Computational biology

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###### Joint Committee for Guides in Metrology

Propagation of distributions using a

**Monte****Carlo****method**.. *JCGM 102:2011. Evaluation of measurement data - Supplement 2 to the ... and a**method**is provided for doing that. This**method**refines the information previously provided in an "error analysis", and ... Evaluation of measurement data - Applications of the least-squares**method**. (planned). *JCGM 108 - Evaluation of measurement ... Evaluation of measurement data - Concepts, principles and**methods**for the expression of measurement uncertainty. (Under ...###### Supercomputer

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###### 易辛模型 - 维基百科，自由的百科全书

7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 Newman MEJ, Barkema GT, "

**Monte****Carlo****Methods**in Statistical Physics, Clarendon Press, 1999 ... 將易辛模型比擬為馬可夫鏈是一件很容易的事情，因為下一刻狀態 ν 的轉移機率 Pβ(ν) 只和目前狀態 μ有關 。事實上，Metropolis 演算法就是馬可夫蒙地卡羅(Markov Chain**Monte****Carlo**)的一個版本。而且因為演算時採用的是單 ... Interactive**Monte****Carlo**simulation of the Ising, XY and Heisenberg models with 3D graphics(###### Business war games

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**method**has been shown to generate significantly better negotiation outcomes compared to other popular

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**method**before deployment.[36] ... Trotman, Ken T. (2005),"Auditor negotiations: An examination of the efficacy of intervention

**methods**".The Accounting Review, ...

###### Provence

Claude Monet (1840-1927) visited Menton, Bordighera, Juan-les-Pins,

**Monte**-**Carlo**, Nice, Cannes, Beaulieu and Villefranche, and ... Since that time, cultivation of poorer varieties has been reduced and new technologies and**methods**have improved the quality ... Edvard Munch (1863-1944) visited and painted in Nice and**Monte**-**Carlo**(where he developed a passion for gambling), and rented a ... Cannes and**Monte****Carlo**, eventually staying at St. Raphaël, where he wrote much of The Great Gatsby and began Tender is the ...###### Nurse with Wound list

La

**Monte**Young, American composer and musician.. Z[edit]. *Frank Zappa, American musician and composer. Was member of the ... Has worked with Steve Lacy (see above),**Carla**Bley, Terje Rypdal (see below), and Robert Wyatt (see below). ... Nu Creative**Methods**, French jazz duo of Bernard Pruvost and Pierre Bastien. ...###### Molecular dynamics

Following the earlier successes of

**Monte****Carlo**simulations, the**method**was first developed by Fermi, Pasta, Ulam and Tsingou[1] ... Shifted force**method**. Parallelization strategiesEdit. *Domain decomposition**method**(Distribution of system data for parallel ... Bartels, Christian (1 December 2000). "Analyzing biased**Monte****Carlo**and molecular dynamics simulations". Chemical Physics ... These**methods**are termed mixed or hybrid quantum-mechanical and molecular mechanics**methods**(hybrid QM/MM).[39] ...###### Flat Earth

Herreria,

**Carla**(2017-04-22). "Neil deGrasse Tyson Cites Celebrity Flat-Earthers To Make A Point About Politics". Huffington ... Fallacara, Giuseppe; Occhinegro, Ubaldo (2013), Manoscritto Voynich e Castel del**Monte**: Nuova chiave interpretativa del ... a**method**similar to Eratosthenes' measurement of the circumference of the Earth, but the Zhoubi Suanjing assumes that the Earth ...**method**. St. Thomas Aquinas (1225-1274), the most widely taught theologian of the Middle Ages, believed in a spherical Earth; ...###### Spatial analysis

The use of Bayesian hierarchical modeling[22] in conjunction with Markov Chain

**Monte****Carlo**(MCMC)**methods**have recently shown ... Initial approaches to CA proposed robust calibration approaches based on stochastic,**Monte****Carlo****methods**.[25][26] ABM ... A recent MPS algorithm used to accomplish this task is the pattern-based**method**by Honarkhah.[29] In this**method**, a distance- ... This**method**is able to quantify the spatial connectivity, variability and uncertainty. Furthermore, the**method**is not sensitive ...###### Neurotoksin

Bergamini,

**Carlo**M., Stefani Gambetti, Alessia Dondi, and**Carlo**Cervellati (2004) "Oxygen, Reactive Oxygen Species and Tissue ... Costa, Lucio G., Gennaro Giordano, and Marina Guizzetti (2011) In Vitro Neurotoxicology:**Methods**and Protocols. New York: ... Chu, Jennifer, Ming Tong, and Suzanne M.**Monte**(2007) "Chronic Ethanol Exposure Causes Mitochondrial Dysfunction and Oxidative ...###### Bayes estimator

Main article: Empirical Bayes

**method**. A Bayes estimator derived through the empirical Bayes**method**is called an empirical Bayes ... Markov chain**Monte****Carlo**. *. Statistics portal. *v. *t. *e. In estimation theory and decision theory, a Bayes estimator or a ... Empirical Bayes**methods**enable the use of auxiliary empirical data, from observations of related parameters, in the development ... and the Bayes estimator cannot usually be calculated without resorting to numerical**methods**. ...**Monte** **Carlo** algorithm - Simple English Wikipedia, the free encyclopedia

**Monte**

**Carlo**

**method**applied to approximating the value of π. After placing 30,000 random points, the probability that the ... A

**Monte**

**Carlo**algorithm is an algorithm for computers which is used to simulate the behaviour of other systems. It is not an ... For example, a

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**Carlo**algorithm would randomly place points in the square and use the percentage of points falling inside of the circle ...

###### Prime number

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**Carlo**O. (. k. (. log. . n. ). 2. +. ε. ). {\displaystyle O(k(\log n)^{2+\varepsilon })}. error probability 4. −. k. {\ ... The most basic

**method**of checking the primality of a given integer n. {\displaystyle n}. is called trial division. This

**method**...

**Monte**

**Carlo**O. (. k. (. log. . n. ). 2. +. ε. ). {\displaystyle O(k(\log n)^{2+\varepsilon })}. error probability 2. −. k. {\ ...

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**Carlo**O. (. (. log. . n. ). 2. +. ε. ). {\displaystyle O((\log n)^{2+\varepsilon })}. [132][133]. ...

###### Numerical weather prediction

Leith, C.E. (June 1974). "Theoretical Skill of

**Monte****Carlo**Forecasts". Monthly Weather Review. 102 (6): 409-418. Bibcode: ... numerical**methods**obtain approximate solutions. Different models use different solution**methods**: some global models and almost ... and proposed using an ensemble of stochastic**Monte****Carlo**simulations to produce means and variances for the state of the ... A variety of**methods**are used to gather observational data for use in numerical models. Sites launch radiosondes in weather ...###### Dudley Moore

The pair closed the decade with appearances in the ensemble caper film

**Monte****Carlo**or Bust and Richard Lester's The Bed Sitting ... The pair developed an unorthodox**method**for scripting the material, using a tape recorder to tape an ad-libbed routine that ...**Monte****Carlo**or Bust! (1969) (aka Those Daring Young Men in Their Jaunty Jalopies) - Lt. Barrington ...###### Molekul

Anderson JB (May 2004). "Comment on "An exact quantum

**Monte****Carlo**calculation of the helium-helium intermolecular potential" [J ... Ellis, Lyndon A; Roberts, David J (1997). "Chromatographic and hyphenated**methods**for elemental speciation analysis in ...###### Evolutionary computation

Fraser AS (1958). "

**Monte****Carlo**analyses of genetic models". Nature. 181 (4603): 208-9. Bibcode:1958Natur.181..208F. doi:10.1038 ... Evolutionary programming was introduced by Lawrence J. Fogel in the US, while John Henry Holland called his**method**a genetic ... Genetic algorithms deliver**methods**to model biological systems and systems biology that are linked to the theory of dynamical ... Artificial evolution became a widely recognised optimisation**method**as a result of the work of Ingo Rechenberg in the 1960s and ...###### Quantum **Monte** **Carlo** **Methods** | SpringerLink

A complementary

**method**is the Quantum**Monte****Carlo****method**which allows the study of much larger systems (of the order of hundred ... K.Binder: in**Monte****Carlo****Methods**in Statistical Physics, ed. by K. Binder Topics in Current Physics, vol. 7 (Springer Verlag, ... Partition Function Projection**Method**Time Slice Trial Function**Monte****Carlo**Sampling These keywords were added by machine and ... Quantum**Monte****Carlo****Methods**, edited by M. Suzuki (Springer-Verlag 1987); D.J. Scalapino, Frontiers and Borderlines in Many- ...###### Sequential **Monte** **Carlo** **methods** continued

**Monte** **Carlo** Simulation with Asymptotic **Method**

We not only provide general scheme of our

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**Monte** **Carlo** and Quasi-**Monte** **Carlo** **Methods** 2006 | SpringerLink

This book represents the refereed proceedings of the Seventh International Conference on

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###### CiteSeerX - Sequential **Monte** **Carlo** **Methods** for Dynamic Systems

A general framework for using

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###### Development of **Monte**-**Carlo** **methods** for edge physics | Max-Planck-Institut für Plasmaphysik

One of the possible approaches to the modeling of heat and particles transport is

**Monte**-**Carlo**. The fluid version of MC is ... Conventional**methods**of computational fluid dynamics are not applicable in this case directly: the problem is numerically stiff ... The advantages of the**method**are obvious: one can model transport phenomena in the magnetic field of (almost) any degree of ...###### Abstract for ``Bayesian Training of Backpropagation Networks
by the Hybrid **Monte** **Carlo** **Method**''

Bayesian Training of Backpropagation Networks by the Hybrid

**Monte****Carlo****Method**Radford M. Neal, Dept. of Computer Science, ... In this work, the Hybrid**Monte****Carlo****method**is implemented in conjunction with simulated annealing, in order to speed ... "Hybrid**Monte****Carlo**"**method**. This approach allows the true predictive distribution for a test case given a set of training cases ... Bayesian training of backpropagation networks by the hybrid**Monte****Carlo****method**appears in the following conference paper: ...SimulationsAlgorithmsMCMCQuantum Monte Carlo MEstimationAlgorithmApproximationCalculationsProbabilityVariancePerturbation Monte-CarloMathematicalElliptic PDEs with Random CoefficientsFinite elemenMultilevel Monte Carlo mOptimizationConvergenceAbstractStandard Monte CarloUncertaintyQuasi-Monte CarloExploring Monte Carlo MLatticePhysicsDownload exploring mEquationsPseudorandom numbersSamplingEstimatorTheoreticalDistributionsDeterministicNanohub.orgModelApplications of Monte Carlo SimuProbabilisticComputationalFrameworkQuantitativeParticlesSimulation methodApproachTechniquesDiffusionReflectance spectraRandom CoefficientsMethodeComputer-simulationQSARPhotonImplementationBayesianRADIOTHERAPYNumerical integrationNuclearMetropolisCalculationIntegrationCorrelationSequential

###### Simulations16

- This website contains a set of 7 simulations and accompanying worksheets that introduce a number of basic Monte Carlo techniques (e.g. generating and testing random sequences, simulating random walks and radioactive decay, and sampling according to a given distribution). (compadre.org)
- This book chapter describes the solution of the Boltzmann transport equation via the MC method and it also presents its application of various types of devices simulations. (nanohub.org)
- Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. (whsmith.co.uk)
- Potential applications of the method to simulations of ring-forming equilibrium polymers, disklike micelles, and self-assembling polymer loops are discussed. (ebscohost.com)
- The bond-scale and chain-scale structure of linear polymers located close to spherical impenetrable surfaces is studied in dense systems by means of lattice Monte Carlo simulations. (ebscohost.com)
- Polymer simulations make extensive use of biased Monte Carlo schemes. (ebscohost.com)
- Single chain in mean field simulations: Quasi-instantaneous field approximation and quantitative comparison with Monte Carlo simulations. (ebscohost.com)
- The description of fluctuations by single chain in mean field (SCMF) simulations is discussed and the results of this particle-based self-consistent field technique are quantitatively compared to Monte Carlo simulations of the same discretized Edwards-Hamiltonian providing exact reference data. (ebscohost.com)
- The present work aims at comparing simulations of photon transport phenomena in biological multi-layered tissues by means of two methods: a finite element code and a Monte Carlo procedure. (spie.org)
- Embodiments relate to systems and methods for validating interpolation results using Monte Carlo simulations on interpolated data inputs. (google.com)
- Monte Carlo simulations are generally used when analytic properties of the model under the specified conditions are not known or are unattainable. (sagepub.com)
- This edition includes a brief overview of other methods of computer simulation and an outlook for the use of Monte Carlo simulations in disciplines beyond physics. (google.com)
- These experimental results are contrasted with simulations based on a limited diffusion aggregation model and Metropolis Monte Carlo. (gob.ar)
- A published and qualified population pharmacokinetic model was used to perform Monte Carlo simulations of ceftazidime concentrations. (nih.gov)
- Predicting isoelectric points of nonfunctional mitochondria from Monte Carlo simulations of surface compositions. (biomedsearch.com)
- Monte Carlo simulations are exploited to assess the annual radiation doses from some cosmetics due to the radioactive decay series of U and Th and to the radionuclide K. The measured radioactivity con. (bioportfolio.com)

###### Algorithms11

- Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. (wikipedia.org)
- For example, the cell modeling software MCell uses Monte Carlo algorithms to track the evolution of biochemical events in space and time for individual molecules. (psc.edu)
- Most commonly used among these is the class of Markov Chain Monte Carlo (MCMC) algorithms, which includes the simple Gibbs sampling algorithm, as well as a family of methods known as Metropolis-Hastings. (coursera.org)
- PELE combines a Monte Carlo stochastic approach with protein structure prediction algorithms, and is capable of accurately reproducing long timescale processes in only few hours of CPU (typically no more than an overnight computing period). (bsc.es)
- However, optical diffusion theory provides an analytic approach that might supersede MC methods due to faster, more efficient algorithms. (spie.org)
- Two Monte Carlo algorithms (dynamic and static) are combined in order to model and simulate the branch distribution and topology of polymer chains synthesized in hyper-branched polymerization of polyethylene with Pd-diimine catalysts. (queensu.ca)
- However, selecting and tuning sampling algorithms suited for a given problem remains challenging and a comprehensive comparison of different methods is so far not available. (biomedcentral.com)
- These results can inform the selection of sampling methods and the benchmark collection can serve for the evaluation of new algorithms. (biomedcentral.com)
- This thesis is devoted to the construction and implementation of algorithms which incorporate the rigid-body approximation into existing Monte Carlo methods for solving the quantum mechanical many-body problem. (uri.edu)
- [3] The main difference between the classical dynamic programming methods and reinforcement learning algorithms is that the latter do not assume knowledge of an exact mathematical model of the MDP and they target large MDPs where exact methods become infeasible. (wikipedia.org)
- To evaluate the feasibility of using MC methods to study properties of real systems, an implementation of the Parallel Tempering Monte Carlo (PTMC) method using state of the art algorithms to perform exchanges, determine the temperature set and adjust the maximum displacement, was built. (usp.br)

###### MCMC13

- When the probability distribution of the variable is parametrized, mathematicians often use a Markov chain Monte Carlo (MCMC) sampler. (wikipedia.org)
- That is, in the limit, the samples being generated by the MCMC method will be samples from the desired (target) distribution. (wikipedia.org)
- In contrast with traditional Monte Carlo and MCMC methodologies, these mean field particle techniques rely on sequential interacting samples. (wikipedia.org)
- Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized statistical computing and have had an especially profound impact on the practice of Bayesian statistics. (ebooks.com)
- Furthermore, MCMC methods have enabled the development and use of intricate models in an astonishing array of disciplines as diverse as. (ebooks.com)
- Since their popularization in the 1990s, Markov chain Monte Carlo (MCMC) methods have revolutionized. (ebooks.com)
- The Markov chain Monte Carlo (MCMC) method is a general simulation method for sampling from posterior distributions and computing posterior quantities of interest. (sas.com)
- MCMC methods sample successively from a target distribution. (sas.com)
- 2004 ) , Robert and Casella ( 2004 ) , and Congdon ( 2001 , 2003 , 2005 ) provide both theoretical and applied treatments of MCMC methods. (sas.com)
- A further application of MCMC methods is made in the area of data analysis for the proposed LISA mission. (gla.ac.uk)
- In particular, Markov chain Monte Carlo (MCMC) methods have become increasingly popular as they allow for a rigorous analysis of parameter and prediction uncertainties without the need for assuming parameter identifiability or removing non-identifiable parameters. (biomedcentral.com)
- Markov chain Monte Carlo (MCMC) techniques can provide estimates of the posterior density of orders while accounting naturally for missing data, data errors and unknown parameters. (semanticscholar.org)
- this is what some people call the Markov-Chain Monte-Carlo, MCMC. (coursera.org)

###### Quantum Monte Carlo M6

- Dzierzawa M., Zotos X. (1990) Quantum Monte Carlo Methods. (springer.com)
- Quantum Monte Carlo Methods in Physics and Chemistry, NATO Science Series C by M.P. Nightingale, 9780792355519. (booktopia.com.au)
- This volume contains lectures on the basic theory and applications of quantum Monte Carlo methods, with contributions written by authorities in the field. (booktopia.com.au)
- The 2016 Talent school on nuclear Quantum Monte Carlo methods will be held at North Carolina State University (NCSU) from Monday July 11 through Friday July 29, 2016. (ncsu.edu)
- The school is intended to introduce students and young researchers to the various facets of Quantum Monte Carlo methods based on stochastic integration, that are used to solve the ground- and low-lying excited states of nuclei and matter. (ncsu.edu)
- The format of the school is unique: in the mornings, students will receive lectures on Quantum Monte Carlo methods applied in nuclear physics. (ncsu.edu)

###### Estimation7

- We use sampling methods to perform model selection and parameter estimation. (aes.org)
- One mecha- nism to make such estimation is Monte Carlo simulation, whose simplest version is crude or standard simulation. (inria.fr)
- The experimental evaluation has been compared to the simulated estimation of the effective area obtained through Monte Carlo method (MCM). (niscair.res.in)
- A`method for the coefficients stability estimation is also described. (mathnet.ru)
- Group object structure and state estimation with evolving networks and Monte Carlo methods. (lancs.ac.uk)
- Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation', Annals of Applied Probability , 24(4):1585-1620, 2014. (ox.ac.uk)
- The PRIMO system is a computer software that allows the Monte Carlo simulation of linear accelerators and the estimation of the subsequent absorbed dose distributions in phantoms and computed tomographies. (biomedcentral.com)

###### Algorithm10

- Through the analysis of differences and connections, we consolidate these methods into a generic algorithm by combining desirable features. (psu.edu)
- Monte-Carlo algorithm. (edwardbetts.com)
- We describe a sequential Monte Carlo (SMC) expectation maximization algorithm that both infers the posterior distributions of the hidden states, and finds the maximum likelihood estimates of the parameters. (cam.ac.uk)
- Finally, to bring out the effectiveness of this method for reconstructing low-scattering objects, we apply a diffusion equation-based algorithm on a dataset from one of the low-scattering objects and show that it fails to reconstruct object inhomogeneities. (spiedigitallibrary.org)
- The work is based on the Markov Chain Monte Carlo algorithm and features enhancements specifically targeted to this problem. (gla.ac.uk)
- The conference reviewed the use of the Metropolis Algorithm and the Monte Carlo Method in the physical sciences, highlighted recent developments, and noted the spread of the Monte Carlo Method to other fields. (alldiscountbooks.net)
- We present the results of a thorough benchmarking of state-of-the-art single- and multi-chain sampling methods, including Adaptive Metropolis, Delayed Rejection Adaptive Metropolis, Metropolis adjusted Langevin algorithm, Parallel Tempering and Parallel Hierarchical Sampling. (biomedcentral.com)
- Purpose: Exploring appropriate offset values in dose optimization with pencil beam (PB) algorithm to minimize dosimetric differences with plans calculated with Monte Carlo (MC) for lung cancer treatment with Stereotactic Body Radiotherapy (SBRT). (osti.gov)
- To evaluate the difference of absorbed doses calculated to medium and to water by a Monte Carlo (MC) algorithm based treatment planning system (TPS), and to assess the potential clinical impact to dose prescri. (biomedcentral.com)
- Here, we develop a Monte Carlo tree search algorithm for grain boundary segregation and apply it to determine the stable segregation configuration of copper Σ5[001]/(210) and Σ37[001]/(750) with silver impurities. (bioportfolio.com)

###### Approximation3

- Though we can only state the upper bound of the approximation error, the convergence rate of quasi-Monte Carlo method in practice is usually much faster than its theoretical bound. (wikipedia.org)
- Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. (ebooks.com)
- Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. (repec.org)

###### Calculations7

- Numerical calculations demonstrating the effectiveness of the method for one- and two-dimensional model problems arising in groundwater flow are presented. (psu.edu)
- From repeated Monte Carlo draws, it becomes possible to quantitatively estimate most likely recurrence PDF parameters, and a ranked distribution of parameters is returned that can be used to assess uncertainties in hazard calculations. (usgs.gov)
- The CORAL software provides the Monte Carlo calculations aimed to build up QSPR/QSAR models for different endpoints. (eurekaselect.com)
- As the computing performance of hardware and software has advanced, Monte Carlo methods have been applied to the nuclear analysis of whole core problems, because the accuracy of the Monte Carlo calculations has been enhanced by its ability to use continuous energy nuclear data and to handle complex geometry information. (scichina.com)
- When approaching whole core analyses, the Monte Carlo criticality calculations must handle some challenging problems, such as slow convergence, the stopping criteria of source convergence, and real variance estimations. (scichina.com)
- The software PRIMO for the Monte Carlo simulation of radiotherapy linacs could potentially act as a independent calculation system to verify the calculations of treatment planning systems. (biomedcentral.com)
- The utility of PEREGRINE Monte Carlo calculations for radiation treatment planning in a clinical setting will be assessed by comparing results with other fully three-dimensional programs. (bioportfolio.com)

###### Probability10

- Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. (wikipedia.org)
- Monte Carlo methods vary, but tend to follow a particular pattern: Define a domain of possible inputs Generate inputs randomly from a probability distribution over the domain Perform a deterministic computation on the inputs Aggregate the results For example, consider a quadrant (circular sector) inscribed in a unit square. (wikipedia.org)
- Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density function (pdf) and cumulative distribution function (cdf) were derived and made available. (ebooks.com)
- Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. (ellibs.com)
- Monte Carlo estimators are constructed as averages over samples drawn from some probability distribution. (uri.edu)
- Since undergrad, I have been very aware of Bayesian methods, and there has always been people in my life calling me to the Bayesian side, saying that the results were easier to interpret, that we get probability for a hypothesis instead of the data given a hypothesis, etc. (stackexchange.com)
- What I kept thinking through Mayo's book was: There is a way we can use computers to make sure our frequentist methods work, because probability is what we see in the long run and we can simulate that. (stackexchange.com)
- How do Bayesians verify that their methods define uncertainty properly (i.e., calculate valid credible intervals and posterior distributions) using Monte Carlo simulation methods, if probability is not defined as rates in the long run? (stackexchange.com)
- After briefly recalling essential background in statistical mechanics and probability theory, it gives a succinct overview of simple sampling methods. (google.com)
- Monte Carlo simulation combines the principles of probability and statistics with the expert opinion and data sources to quantify the uncertainty associated with the real systems. (environmental-expert.com)

###### Variance8

- We shall propose a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance. (repec.org)
- It contains standard material usually considered in Monte Carlo simulation as well as new material such as variance. (ebooks.com)
- The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output. (whsmith.co.uk)
- Introduction Generating random numbers Variance reduction techniques Markov chain Monte Carlo Statistical analysis of simulation output The Ising model and related examples Bibliography. (whsmith.co.uk)
- In this thesis some existing methods to improve the standard simulation in the context of rare events are analyzed, some variance analyses are made and the methods are tested empirically over a variety of models. (inria.fr)
- Giles' method requires estimates for the variance of g(XT) − g(Xπ. (psu.edu)
- The purpose of this study was to assess the performance of the LRT[subscript k] and the [delta subscript k] when violating the assumptions underlying the RI strategy and/or the factor variance scaling method. (utexas.edu)
- Here, the theory and challenges of Monte Carlo criticality are introduced, and progress in convergence acceleration methods and variance reduction techniques is reviewed. (scichina.com)

###### Perturbation Monte-Carlo2

- Yalavarthy Phaneendra Kumar , Ram M. Vasu , "Reconstruction of optical properties of low-scattering tissue using derivative estimated through perturbation Monte-Carlo method," Journal of Biomedical Optics 9(5), (1 September 2004). (spiedigitallibrary.org)
- In the second step, another set of photon trajectory information, including the locations of all collision events from the baseline simulation and the scaling result obtained from the first step, is employed by the perturbation Monte Carlo method to estimate diffuse reflectance from the multilayered tissue model with tumor-like heterogeneities. (spiedigitallibrary.org)

###### Mathematical11

- The Quasi-Monte Carlo method recently became popular in the area of mathematical finance or computational finance. (wikipedia.org)
- Finally, we show mathematical validity of our method. (repec.org)
- Monte Carlo calculation of photon transport is based on stochastic mathematical simulation of the interactions between photons and matter (for a review and general references on Monte Carlo techniques see, e.g. (stuk.fi)
- A computer-simulation technique that uses random samples and other statistical methods to find approximate solutions to mathematical or physical problems. (yourdictionary.com)
- This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. (whsmith.co.uk)
- Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. (whsmith.co.uk)
- Methods: Molecular descriptors are a mathematical function of so-called correlation weights of various molecular features. (eurekaselect.com)
- Pricing high-dimensional American-style derivatives is still a challenging task, as the complexity of numerical methods for solving the underlying mathematical problem rapidly grows with the number of uncertain factors. (uni-koeln.de)
- Now, I also love R and using simulation methods to verify that methods work makes way more sense to me than mathematical proofs (again: background in a quantitative social science, not theoretical statistics). (stackexchange.com)
- This textbook presents the application of mathematical methods and theorems tosolve engineering problems, rather than focusing on mathematical proofs. (springer.com)
- The first step to the Monte Carlo process is to build a mathematical model with a set of relationships that simulates a real system. (environmental-expert.com)

###### Elliptic PDEs with Random Coefficients2

- K.A. Cliffe, M.B. Giles, R. Scheichl, A.L. Teckentrup, 'Multilevel Monte Carlo Methods and Applications to Elliptic PDEs with Random Coefficients', Computing and Visualization in Science , 14(1):3-15, 2011. (ox.ac.uk)
- Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients', Numerische Mathematik , 125(3):569-600, 2013. (ox.ac.uk)

###### Finite elemen2

- It is shown that for first order finite elements in two space dimensions, the multilevel Monte Carlo finite element method converges at the same rate as the corresponding single-level Monte Carlo finite element method, despite the majority of samples being underresolved in the multilevel Monte Carlo finite element estimator. (epfl.ch)
- It is proved that switching to a hierarchic multiscale finite element method such as the finite element heterogeneous multiscale method to compute the multilevel Monte Carlo finite element estimator, when only meshes are used which underresolve all physical length scales, implies optimal convergence. (epfl.ch)

###### Multilevel Monte Carlo m2

###### Optimization12

- In the current study, Monte Carlo optimization based Quantitative Structure Toxicity Relationship (QSTR) analyses were performed on a dataset containing diverse chemical pesticides with toxicity data determined on Bobwhite quail. (igi-global.com)
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- The interpretation is calculated on results of several runs of the Monte Carlo optimization. (eurekaselect.com)
- Perturbatively selected configuration-interaction wave functions for efficient geometry optimization in quantum Monte Carlo. (bioportfolio.com)

###### Convergence5

- Quasi-Monte Carlo has a rate of convergence close to O(1/N), whereas the rate for the Monte Carlo method is O(N−0.5). (wikipedia.org)
- Therefore, we show the statistical equivalence of the four methods and some of their convergence characteristics. (spie.org)
- The convergence of multilevel Monte Carlo finite element discretizations is analyzed. (epfl.ch)
- 1. Whereas the PMC gives an accurate and quick method for constructing the Jacobian the same, when adapted to update the computed projection data, the data are not accurate enough for use in the iterative reconstruction procedure leading to convergence. (spiedigitallibrary.org)
- Monte Carlo methods provide a way to estimate these integrals by statistically sampling a subset of configuration space, and these methods provide 1/√ N convergence regardless of dimension. (uri.edu)

###### Abstract1

- Abstract: A Monte Carlo Potts′ model with different ratios of grain boundary energy is proposed for the sintering process of two-phase nanocomposite ceramic materials. (scientific.net)

###### Standard Monte Carlo2

- The standard Monte Carlo method is frequently used when the quadrature methods are difficult or expensive to implement. (wikipedia.org)
- In the paper, Halton, Sobol, and Faure sequences for quasi-Monte Carlo are compared with the standard Monte Carlo method using pseudorandom sequences. (wikipedia.org)

###### Uncertainty3

- The method has been applied to a test problem, demonstrating that it can produce good predictions, as well as an indication of the uncertainty of these predictions. (utoronto.ca)
- The measurement uncertainties have been calculated using the conventional method, i.e., law of propagation of uncertainty (LPU) as well as MCM. (niscair.res.in)
- This evolving graph model is propagated combined with a sequential Monte Carlo framework able to cope with measurement origin uncertainty. (lancs.ac.uk)

###### Quasi-Monte Carlo22

- In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences). (wikipedia.org)
- Monte Carlo and quasi-Monte Carlo methods are stated in a similar way. (wikipedia.org)
- The difference between quasi-Monte Carlo and Monte Carlo is the way the xi are chosen. (wikipedia.org)
- Quasi-Monte Carlo uses a low-discrepancy sequence such as the Halton sequence, the Sobol sequence, or the Faure sequence, whereas Monte Carlo uses a pseudorandom sequence. (wikipedia.org)
- Hence, the Monte Carlo method and the quasi-Monte Carlo method are beneficial in these situations. (wikipedia.org)
- Hence, in general, the accuracy of the quasi-Monte Carlo method increases faster than that of the Monte Carlo method. (wikipedia.org)
- Monte Carlo and quasi-Monte Carlo methods are accurate and relatively fast when the dimension is high, up to 300 or higher. (wikipedia.org)
- Morokoff and Caflisch studied the performance of Monte Carlo and quasi-Monte Carlo methods for integration. (wikipedia.org)
- However, Morokoff and Caflisch gave examples where the advantage of the quasi-Monte Carlo is less than expected theoretically. (wikipedia.org)
- Still, in the examples studied by Morokoff and Caflisch, the quasi-Monte Carlo method did yield a more accurate result than the Monte Carlo method with the same number of points. (wikipedia.org)
- Morokoff and Caflisch remark that the advantage of the quasi-Monte Carlo method is greater if the integrand is smooth, and the number of dimensions s of the integral is small. (wikipedia.org)
- Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. (booktopia.com.au)
- This volume contains the refereed proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. (booktopia.com.au)
- These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods. (booktopia.com.au)
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- 343-358, in Monte Carlo and Quasi-Monte Carlo Methods 2006 , Springer, 2008. (ox.ac.uk)
- It uses randomised quasi-Monte Carlo techniques based on a rank-1 lattice rule to further improve the computational efficiency. (ox.ac.uk)
- Multilevel path simulation for jump-diffusion SDEs', pp.695-708 in Monte Carlo and Quasi-Monte Carlo Methods 2010 , Springer, 2012. (ox.ac.uk)
- Computing Greeks using multilevel path simulation', pp.281-296 in Monte Carlo and Quasi-Monte Carlo Methods 2010 , Springer, 2012. (ox.ac.uk)

###### Exploring Monte Carlo M4

- Exploring Monte Carlo Methods is a basic text that describes the numerical methods that have come to be known as "Monte Carlo. (ebooks.com)
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###### Lattice2

- Those methods are essentially based on projection in imaginary time, and are formulated either in coordinate space and/or on lattice. (ncsu.edu)
- The main methods that will be covered during the school are the Green's Function Monte Carlo (GFMC), the Auxiliary Field Diffusion Monte Carlo (AFDMC), and Lattice Auxiliary Field methods. (ncsu.edu)

###### Physics5

- In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean-Vlasov processes, kinetic models of gases). (wikipedia.org)
- S. Wheaton, Computer Program COMPUTATIONAL PHYSICS RESOURCES: BASIC MONTE CARLO METHODS (2014), WWW Document, ( https://www.compadre.org/Repository/document/ServeFile.cfm?ID=13108&DocID=3659 ). (compadre.org)
- Computational Physics Resources: Basic Monte Carlo Methods [Computer software]. (compadre.org)
- books.google.com - This new and updated edition deals with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics, statistical mechanics, and related fields. (google.com)
- PRIMO is a dose verification system based on the general-purpose Monte Carlo radiation transport code penelope , which implements an accurate physics model of the interaction cross sections and the radiation trans. (biomedcentral.com)

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###### Equations1

- This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. (springer.com)

###### Pseudorandom numbers1

- This is in contrast to the regular Monte Carlo method or Monte Carlo integration, which are based on sequences of pseudorandom numbers. (wikipedia.org)

###### Sampling7

- All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. (psu.edu)
- Many of the Monte Carlo methods and practices used to be referred to as rather generic "statistical sampling. (yourdictionary.com)
- EJS model for the Sampling Rejection Method Model worksheet. (compadre.org)
- In particular, it is considered that the multilevel finite element discretization resolves the finest physical length scale, but the coarsest finite element mesh does not, so that the so-called resonance case occurs at intermediate multilevel Monte Carlo sampling levels. (epfl.ch)
- Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample subject to fixed constraints. (newton.ac.uk)
- The availability of both, benchmark problems and toolboxes, is more problematic for sampling methods. (biomedcentral.com)
- To the best of our knowledge, there is no collection of benchmarking problems for sampling methods featuring dynamical systems. (biomedcentral.com)

###### Estimator2

- A general method for debiasing a Monte Carlo estimator ," Papers 1005.2228, arXiv.org, revised Jun 2010. (repec.org)
- We propose the split exponential track length estimator (seTLE), a new kerma-based method combining the exponential variant of the TLE and a splitting strategy to speed up Monte Carlo (MC) dose computation for low energy photon beams. (nih.gov)

###### Theoretical2

- It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. (whsmith.co.uk)
- The hereto presented theoretical grounds of the methods make it possible to consider uncertainties in the assessment of input data values. (sae.org)

###### Distributions2

- PRIMO is a software system based on the Monte Carlo method that simulates linacs and absorbed dose distributions in external beam radiotherapy patients. (biomedcentral.com)
- The main applications of these methods will be deeply discussed during the school, including the calculation of properties of nuclei (energies, radii, distributions, transitions) and the equation of state of neutron matter. (ncsu.edu)

###### Deterministic6

- These methods are often used when others fail, since they are much less sensitive to the 'curse of dimensionality', which plagues deterministic methods in problems with a large number of variables. (whsmith.co.uk)
- Specifically, both methods proposed here allow one to obtain estimates of the expectation of the random solution, with accuracy versus work that is identical to the solution of a single deterministic problem. (epfl.ch)
- The advantages and disadvantages of the two major categories of numerical methods, deterministic and stochastic approaches, in polymer reaction engineering are discussed. (queensu.ca)
- A hybrid deterministic/stochastic approach and a combined stochastic/stochastic method are developed to represent two polymerization systems of interest. (queensu.ca)
- A deterministic model is formulated to separately track the homopolymer chains that are produced without the desired functionality, a Monte Carlo (MC) model is written to represent the system, and a hybrid deterministic/MC approach is taken using new capabilities within the software package PREDICI. (queensu.ca)
- [5] Generally speaking, the Monte Carlo method is a statistical approach to solve deterministic many-body problems. (wikipedia.org)

###### Nanohub.org1

- David K. Ferry (2008), "Ensemble Monte Carlo Method Described," https://nanohub.org/resources/4439. (nanohub.org)

###### Model17

- EJS model to accompany the Transformation Method worksheet. (compadre.org)
- the author notes that the text is intended for users who want to know more about how the Monte Carlo model "does what it does. (springer.com)
- The forward model is based on Monte Carlo simulation to calculate the diffuse light flux on the surface of the mouse. (niscair.res.in)
- An iterative method for the reconstruction of optical properties of a low-scattering object, which uses a Monte-Carlo-based forward model, is developed. (spiedigitallibrary.org)
- We present two Monte Carlo methods for estimating workload of a driver in real-time, based on a driver model developed in a cognitive architecture. (offis.de)
- Here, we use a tailor-made Monte Carlo type program that fits the whole MALDI spectrum and generates a 3D model of the ligand shell. (epfl.ch)
- Quantitative description of the ligand shell in terms of nearest neighbor distribution and characteristic length scale can be readily extracted by the model, and are compared with the results of other characterization methods. (epfl.ch)
- We present a hybrid method that combines a multilayered scaling method and a perturbation method to speed up the Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with finite-size tumor-like heterogeneities. (spiedigitallibrary.org)
- In the first step, a set of photon trajectory information generated from a baseline Monte Carlo simulation is utilized to scale the exit weight and exit distance of survival photons for the multilayered tissue model. (spiedigitallibrary.org)
- 2 In this situation, the Monte Carlo (MC) method provides a flexible tool to model light transport. (spiedigitallibrary.org)
- Since the MC method can solve a radiative transport equation with any accuracy 3 for a complex tissue model and probe geometry, it is considered the gold standard for modeling light transport in turbid media. (spiedigitallibrary.org)
- 5 proposed a perturbation Monte Carlo (pMC) method to solve inverse photon migration problems in a two-layered tissue model based on spatially resolved diffuse reflectance and validated this method experimentally. (spiedigitallibrary.org)
- 6 To our best knowledge, there has been no effort in the literature to speed up the MC method in a multilayered tissue model with finite-size tumor-like heterogeneities. (spiedigitallibrary.org)
- Theoretically, the pMC method may be used in this case, but the applicable range of optical properties in the tissue model and the heterogeneity will be limited. (spiedigitallibrary.org)
- A Monte Carlo simulation is a methodological technique used to evaluate the empirical properties of some quantitative method by generating random data from a population with known properties, fitting a particular model to the generated data, collecting relevant information of interest, and replicating the entire procedure a large number of times (e.g., 10,000) in order to obtain properties of the fitted model under the specified condition(s). (sagepub.com)
- Simulation of full-core pin-by-pin model by JMCT Monte Carlo neutron-photon transport code. (scichina.com)
- To model the effect of surface composition on pI heterogeneity of these mitochondria, we devised a method to predict mitochondrial pI values using simulated surface compositions. (biomedsearch.com)

###### Applications of Monte Carlo Simu2

- In an attempt to focus attention on a manageable set of applications, the main thrust of this book is to emphasize applications of Monte Carlo simulation methods in biology and medicine. (intechopen.com)
- It is hoped that this textbook will help formalize the many existing applications of Monte Carlo simulation and assist in their integration in teaching programs. (springer.com)

###### Probabilistic1

- In principle, Monte Carlo methods can be used to solve any problem having a probabilistic interpretation. (wikipedia.org)

###### Computational6

- One purpose of the multilevel Monte Carlo method is to approximate the expected payoff of an option with a small computational cost. (psu.edu)
- We show how to extend a recently proposed multilevel Monte Carlo approach to the continuous time Markov chain setting, thereby greatly lowering the computational complexity needed to compute expected values of functions of the state of the system to a specified accuracy. (psu.edu)
- It presents numerical results for SDEs using an Euler discretisation, but also analyses the computational complexity for a general class of methods and applications, assuming that the discretisation satisfies certain conditions. (ox.ac.uk)
- This is a survey article looking at the application of multilevel methods in computational finance. (ox.ac.uk)
- Development of numerical tools based on Monte Carlo integrations in combination with the growth of computational facilities opened the way to accurately investigate properties of nuclear systems, including finite nuclei and homogeneous matter. (ncsu.edu)
- Molecular dynamics have been used for the computational study of thermodynamic properties of various nanomaterials, while the use of Monte Carlo methods (MC), in this context, has been restricted to the study of Lennard-Jones (LJ) nanoclusters. (usp.br)

###### Framework2

- A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. (psu.edu)
- We formulate a general, arbitrary-order stochastic response formalism within the Full Configuration Interaction Quantum Monte Carlo framework. (bioportfolio.com)

###### Quantitative2

- Improvements in and availability of high-speed digi- tal computers have created the opportunity to analyze many of these prob- lems using stochastic simulation methods and over the last decade there has been increased interest in and use made of Monte Carlo simulation in quantitative power system reliability assessment. (springer.com)
- For the development of predictive models in a form of the quantitative structure-property / activity relationships (QSPRs/QSARs), the Monte Carlo approach also can be useful. (eurekaselect.com)

###### Particles2

- One of the possible approaches to the modeling of heat and particles transport is Monte-Carlo. (mpg.de)
- Some of us was the citations planets we was would drain more about ebook monte carlo methods in and particles, biogeochemical, current. (theintuitivedecision.com)

###### Simulation method1

- The aim of the paper was to present a method of collision reconstruction calculation using the principle of conservation of momentum, the principle of energy conservation, and the principle of kinetic energy and work equivalence (energy balance) (Marquard), taking into consideration Monte Carlo simulation method. (sae.org)

###### Approach11

- Some factors were studied in this paper based on the Monte Carlo approach. (safetylit.org)
- A quick way to construct and update the Jacobian needed to reconstruct a discretized object, based on the perturbation Monte-Carlo (PMC) approach, is demonstrated. (spiedigitallibrary.org)
- This approach could become the routine method to characterize the ligand shell morphology of many nanoparticles and we provide an open access program to facilitate its use. (epfl.ch)
- Therefore a Monte Carlo approach may be useful for assessing recurrence from limited paleoearthquake records. (usgs.gov)
- I can Learn you the download the cross entropy method a unified approach to combinatorial century list. (deadbatteries.com)
- Visigothic download the cross entropy method a unified approach to combinatorial is rapidly made on finding men even and feeling Social harsh proposals. (deadbatteries.com)
- In 496 the studies sank recognized to download the cross entropy method a unified approach to combinatorial, but unlike the articles they developed pathological trespasses. (deadbatteries.com)
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- Rank's download the cross entropy method a unified approach to combinatorial is Tree-based, a weak 86 intentions. (deadbatteries.com)
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- conquered PurchaseI had that I would be more download the cross entropy method a unified approach about what the Double commands, but it is more like a everyone of programmes, children and years about that discipline and a especially direct period. (deadbatteries.com)

###### Techniques3

- Essentials of Monte Carlo Simulation focuses on the fundamentals of Monte Carlo methods using basic computer simulation techniques. (springer.com)
- Density-of-States Based Monte Carlo Techniques for Simulation of Proteins and Polymers. (ebscohost.com)
- Combinations of methods are suggested in order to take advantage of both techniques. (queensu.ca)

###### Diffusion5

- It is similar to Diffusion Monte Carlo, except that it works with paths rather than points. (edwardbetts.com)
- Diffusion Monte Carlo (DMC) or diffusion quantum Monte Carlo is a quantum Monte Carlo method that uses a Green's function to solve the Schrödinger equation. (edwardbetts.com)
- We develop a simple Monte Carlo method to compute the position at a given time of a diffusion on a graph, with constant speed on each edge. (degruyter.com)
- Diffuse skin reflectance in the 400-800 nm wavelength range was simulated by Monte Carlo and diffusion theory. (spie.org)
- Spectra from diffusion theory were within 5% of the MC results, and the fit between the two methods was further improved by scaling the dermal absorption parameters with a constant factor. (spie.org)

###### Reflectance spectra1

- 4 presented a scaling method for fast MC simulation of diffuse reflectance spectra from multilayered turbid media. (spiedigitallibrary.org)

###### Random Coefficients1

- In this paper Monte Carlo finite element approximations for elliptic homogenization problems with random coefficients, which oscillate on n is an element of N a priori known, separated microscopic length scales, are considered. (epfl.ch)

###### Methode3

- authors) [French] Les deux codes presentes dans ce rapport permettent la determination des coefficients de multiplication de milieux contenant des matieres fissiles sous des formes tres variees et divisees, ils reposent sur la methode de Monte-Carlo. (osti.gov)
- Zum einen erweitern wir die bedeutende Klasse regressionsbasierter Monte-Carlo Methoden um unsere eigens konzipierte Robuste-Regression-Monte-Carlo (RRM) Methode. (uni-koeln.de)
- Der Vergleich unserer Methode mit der in der Praxis fest etablierten Least-Squares-Monte-Carlo (LSM) Methode von Longstaff und Schwartz (2001) liefert uns Speed-Up-Faktoren der Größe vier und höher. (uni-koeln.de)

###### Computer-simulation1

- A new method is proposed for calculation of the chemical potential of macromolecules by computer simulation. (ebscohost.com)

###### QSAR2

- Conclusion: The Monte Carlo technique available via the CORAL software can be a useful and convenient tool for the QSPR/QSAR analysis. (eurekaselect.com)
- Nikolić, G.M. QSAR models for the reactivation of sarin inhibited acetylcholinesterase by quaternary pyridinium oximes based on Monte Carlo method. (eurekaselect.com)

###### Photon1

- The availability of photon and electron spectra in digital form from current accelerators and Monte Carlo (MC) systems is scarce, and one of the packages widely used refers to linacs with a reduced clinical us. (biomedcentral.com)

###### Implementation5

- In this presentation we give an overview of the implementation details of the Ensemble Monte Carlo method for mobility and drift velocity calculation in arbitrary materials and arbitrary crystalographic orientations. (nanohub.org)
- In order to guarantee an efficient implementation of our RRM method, we suggest a new Newton-Raphson-based solver for robust regression with very good numerical properties. (uni-koeln.de)
- If this distribution is the dominant eigenstate of some known operator then a stochastic implementation of the power method can be used to generate the required samples. (uri.edu)
- For rigid bodies, this method involves the implementation of rotational Brownian motion. (uri.edu)
- The method described above can be generalized to investigate excited state properties using correlation function Monte Carlo which is a Monte Carlo implementation of the Rayleigh-Ritz variational method. (uri.edu)

###### Bayesian2

- It is shown that Bayesian training of backpropagation neural networks can feasibly be performed by the "Hybrid Monte Carlo" method. (utoronto.ca)
- The Markov chain method has been quite successful in modern Bayesian computing. (sas.com)

###### RADIOTHERAPY3

- Hence, the contribution of volumes such as collimators, treatment couch and holding devices can be taken into account in the dose calculation.We evaluated and analysed the seTLE method for two realistic small animal radiotherapy treatment plans. (nih.gov)
- Monte Carlo simulation is the state-of-the-art for the study of radiation transport problems in radiotherapy, in particular for modelling medical linear accelerators (linacs). (biomedcentral.com)
- The use of the Monte Carlo (MC) method in radiotherapy dosimetry has increased almost exponentially in the last decades. (biomedcentral.com)

###### Numerical integration2

- After learning about integrating by using antiderivatives, we explored numerical integration with the Trapezoid Method and Simpson's Rule. (wolfram.com)
- A common use of the Monte Carlo method is to perform numerical integration on a function that may be difficult to integrate analytically. (cartesianfaith.com)

###### Nuclear3

- CAD-based Monte Carlo program for integrated simulation of nuclear system superMC. (scichina.com)
- In: Proceedings of Supercomputing in nuclear applications & Monte Carlo, Tokyo, 2010. (scichina.com)
- In the afternoons, there will be hands-on activities, where students will be deeply involved in developing and/or extending Monte Carlo codes to solve some simple system using realistic nuclear Hamiltonians. (ncsu.edu)

###### Metropolis2

- At Los Alamos, in the 1950s, a group of researchers led by Metropolis, including John von Neumann and Stanislaw Ulam , developed the Monte Carlo method . (wikipedia.org)
- In 1953 Metropolis co-authored the first paper on a technique that was central to the method now known as simulated annealing . (wikipedia.org)

###### Calculation2

- Small angle scattering, Monte Carlo calculation of the interparticle interference [4]. (iucr.org)
- Since we wanted to test the accuracy and precision of the method, it was necessary to design a program that would perform the procedure several times with varying numbers of random points for each calculation. (wolfram.com)

###### Integration2

- For one-dimensional integration, quadrature methods such as the trapezoidal rule, Simpson's rule, or Newton-Cotes formulas are known to be efficient if the function is smooth. (wikipedia.org)
- Monte Carlo, as in Monte Carlo integration, is mainly used to approximate an expectation by using the Markov chain samples. (sas.com)

###### Correlation3

- After compression of the bicrystal up to 5% deformation the strain mapping were characterized by using digital image correlation (DIC) technique and the 2D strain filed provided data to simulate grain growth using a modified Monte Carlo method. (scientific.net)
- W. L. Lin and J. C. Kuo, "On Strain-Induced Grain Growth Using Modified Monte Carlo Method and Digital Image Correlation Technique", Materials Science Forum, Vols. (scientific.net)
- The numerical data on the correlation weights are calculated by the Monte Carlo method. (eurekaselect.com)

###### Sequential1

- You just viewed Sequential Monte Carlo methods... . (merlot.org)