Preconditioning of Markov Chain Monte Carlo Simulations Using

... porosity) realizations adequately reflect the uncertainty in the reservoir properties, i.e., the probability distribution is sampled correctly. This problem is challenging because the permeability field is a function defined on a large number of grid blocks. The Markov chain Monte Carlo (MCMC) metho ...

... porosity) realizations adequately reflect the uncertainty in the reservoir properties, i.e., the probability distribution is sampled correctly. This problem is challenging because the permeability field is a function defined on a large number of grid blocks. The Markov chain Monte Carlo (MCMC) metho ...

Adaptive stochastic-deterministic chemical kinetic simulations

... scales of biological models. The simplest simulation was of end-product inhibition. The medium model was the cyclic adenosine monophosphate (cAMP) signaling pathway (Bhalla, 2002b). The large model was of synaptic signaling (Bhalla, 2002a). The latter two models are based on biochemical parameters f ...

... scales of biological models. The simplest simulation was of end-product inhibition. The medium model was the cyclic adenosine monophosphate (cAMP) signaling pathway (Bhalla, 2002b). The large model was of synaptic signaling (Bhalla, 2002a). The latter two models are based on biochemical parameters f ...

Chapter 6: Monte Carlo Methods for Inferential Statistics

... Methods in inferential statistics are used to draw conclusions about a population and to measure the reliability of these conclusions using information obtained from a random sample. Inferential statistics involves techniques such as estimating population parameters using point estimates, calculatin ...

... Methods in inferential statistics are used to draw conclusions about a population and to measure the reliability of these conclusions using information obtained from a random sample. Inferential statistics involves techniques such as estimating population parameters using point estimates, calculatin ...

Introduction to Bayesian Analysis Procedures

... and obtain p. jy/. These are the essential elements of the Bayesian approach to data analysis. In theory, Bayesian methods offer simple alternatives to statistical inference—all inferences follow from the posterior distribution p. jy/. In practice, however, you can obtain the posterior distribut ...

... and obtain p. jy/. These are the essential elements of the Bayesian approach to data analysis. In theory, Bayesian methods offer simple alternatives to statistical inference—all inferences follow from the posterior distribution p. jy/. In practice, however, you can obtain the posterior distribut ...

Efficient construction of reversible jump Markov chain Monte Carlo

... a procedure for reassigning rejected moves by sequentially attempting further proposals using a modiﬁcation of the usual accept–reject mechanism. This procedure allows some level of adaptation in the sense that later proposals at any particular iteration can be allowed to use information gained from ...

... a procedure for reassigning rejected moves by sequentially attempting further proposals using a modiﬁcation of the usual accept–reject mechanism. This procedure allows some level of adaptation in the sense that later proposals at any particular iteration can be allowed to use information gained from ...

Random Number Generation

... • Application of Random Numbers – Simulation • Simulate natural phenomena – Sampling • It is often impractical to examine all possible cases, but a random sample will provide insight into what constitutes typical behavior – Numerical analysis – Computer programming – Decision making • “Many executiv ...

... • Application of Random Numbers – Simulation • Simulate natural phenomena – Sampling • It is often impractical to examine all possible cases, but a random sample will provide insight into what constitutes typical behavior – Numerical analysis – Computer programming – Decision making • “Many executiv ...

A Simulation Approach to Optimal Stopping Under Partial Information

... frameworks. When the transition density of the state variables is known, classical (a) dynamic programming computations are possible, see e.g. [38]. If the problem state is low-dimensional and Markov, one may alternatively use the quasi-variational formulation to obtain a free-boundary partial diffe ...

... frameworks. When the transition density of the state variables is known, classical (a) dynamic programming computations are possible, see e.g. [38]. If the problem state is low-dimensional and Markov, one may alternatively use the quasi-variational formulation to obtain a free-boundary partial diffe ...

4471 Session 4: Numerical Simulations

... • Could in principle select states completely at random (with uniform probability) - but this would very often pick a high-energy state with negligible probability of occurrence • Instead, arrange that each state r is selected with a probability equal to its probability Pr of appearing in thermal eq ...

... • Could in principle select states completely at random (with uniform probability) - but this would very often pick a high-energy state with negligible probability of occurrence • Instead, arrange that each state r is selected with a probability equal to its probability Pr of appearing in thermal eq ...

P-Value Approximations for T-Tests of Hypothesis

... hypothesis, these assumptions are not verified. 6. Usefulness of the t-test of hypothesis The t-test of hypothesis is a valuable inferential technique for research experiments where the sample size is small or where the population variance or standard deviation is unknown. The study of statistics en ...

... hypothesis, these assumptions are not verified. 6. Usefulness of the t-test of hypothesis The t-test of hypothesis is a valuable inferential technique for research experiments where the sample size is small or where the population variance or standard deviation is unknown. The study of statistics en ...

Correlated Random Variables in Probabilistic Simulation

... There are generally two problems related to statistical correlation: First, during sampling undesired correlation can be introduced between random variables (columns in Table 1). For example instead a correlation coefficient zero for uncorrelated random variables undesired correlation, e.g. 0.6 can ...

... There are generally two problems related to statistical correlation: First, during sampling undesired correlation can be introduced between random variables (columns in Table 1). For example instead a correlation coefficient zero for uncorrelated random variables undesired correlation, e.g. 0.6 can ...

SPECTR1

... simulate complex situations by means of stochastic variables are called Monte Carlo simulations. One can use the Monte Carlo simulation to simulate a manufacturing process, a queueing process, the life cycle of a vehicle, or almost any well-defined process. The Monte Carlo simulation is a very power ...

... simulate complex situations by means of stochastic variables are called Monte Carlo simulations. One can use the Monte Carlo simulation to simulate a manufacturing process, a queueing process, the life cycle of a vehicle, or almost any well-defined process. The Monte Carlo simulation is a very power ...

PRODUCTIONS/OPERATIONS MANAGEMENT

... Can the “state” change continuously or only at discrete points in time? ...

... Can the “state” change continuously or only at discrete points in time? ...

Molecular dynamics simulation

... – That is, the probability of observing a particular arrangement of atoms is a function of the potential energy – In reality, one often does not simulate long enough to reach all energetically favorable arrangements – This is not the only way to explore the energy surface (i.e., sample the Boltzmann ...

... – That is, the probability of observing a particular arrangement of atoms is a function of the potential energy – In reality, one often does not simulate long enough to reach all energetically favorable arrangements – This is not the only way to explore the energy surface (i.e., sample the Boltzmann ...

Filtering Actions of Few Probabilistic Effects

... computing the probability of a posterior given past actions and observations Much faster than an exact algorithm More accurate than particle filtering FO filtering needs less samples than propositional sampling Sampling/Resampling algorithms ...

... computing the probability of a posterior given past actions and observations Much faster than an exact algorithm More accurate than particle filtering FO filtering needs less samples than propositional sampling Sampling/Resampling algorithms ...

Likelihood Fits

... If ∆M >> σM, constraint will dominate, and you might as well just fix M to M0. For example, you never see a constrained fit to h in an HEP experiment. If ∆M << σM, constraint does very little. You have a better measurement than the PDG. You should do an unconstrained fit and PUBLISH. Constrained fit ...

... If ∆M >> σM, constraint will dominate, and you might as well just fix M to M0. For example, you never see a constrained fit to h in an HEP experiment. If ∆M << σM, constraint does very little. You have a better measurement than the PDG. You should do an unconstrained fit and PUBLISH. Constrained fit ...

Stochastic Analog Circuit Behavior Modeling by Point Estimation

... critical but missing link here is how to find an efficient yet accurate mapping between parameter space and performance space. Note that the local random or stochastic variation is the most difficult one to be calculated, which is also called mismatch for the behavior modeling of analog circuits. In ...

... critical but missing link here is how to find an efficient yet accurate mapping between parameter space and performance space. Note that the local random or stochastic variation is the most difficult one to be calculated, which is also called mismatch for the behavior modeling of analog circuits. In ...

Statistics 580 Monte Carlo Methods Introduction

... distribution of T is unknown, the value of c has been determined such that the asymptotic type I error rate is α = .05, (say), i.e., P r(T ≥ c|H0 is true) = .05 as n → ∞. We can study the actual small sample behavior of T by the following procedure: a. generate x1 , x2 , . . . , xn from the appropri ...

... distribution of T is unknown, the value of c has been determined such that the asymptotic type I error rate is α = .05, (say), i.e., P r(T ≥ c|H0 is true) = .05 as n → ∞. We can study the actual small sample behavior of T by the following procedure: a. generate x1 , x2 , . . . , xn from the appropri ...

CS 294-5: Statistical Natural Language Processing

... Let s be a sequence of dice rolls and Chance and Community Chest cards Given s, the outcome V(s) is determined (1 for a win, 0 for a loss) Probability that A wins is s P(s) V(s) ...

... Let s be a sequence of dice rolls and Chance and Community Chest cards Given s, the outcome V(s) is determined (1 for a win, 0 for a loss) Probability that A wins is s P(s) V(s) ...

PDF

... probabilistic analysis methods suitable for use with complex numerical models is needed. An established method of accounting for uncertainties is based on a factor-of-safety approach. However, this approach generally leads to overconservative and hence uneconomical designs. Furthermore, the maximum ...

... probabilistic analysis methods suitable for use with complex numerical models is needed. An established method of accounting for uncertainties is based on a factor-of-safety approach. However, this approach generally leads to overconservative and hence uneconomical designs. Furthermore, the maximum ...

Unlicensed-7-PDF801-804_engineering optimization

... problems. During practical computations, it is important to note that a method that works well for a given class of problems may work poorly for others. Hence it is usually necessary to try more than one method to solve a particular problem efficiently. Further, the efficiency of any nonlinear progr ...

... problems. During practical computations, it is important to note that a method that works well for a given class of problems may work poorly for others. Hence it is usually necessary to try more than one method to solve a particular problem efficiently. Further, the efficiency of any nonlinear progr ...

Basic Skills for the Practical Part of the IBO The IBO practical

... The IBO practical examination should concentrate on the evaluation of competitors for their ability to solve given biological problems using the following skills: In the IBO tasks the names of organisms will be the national names (no description) together with the scientific names (Latin) in bracket ...

... The IBO practical examination should concentrate on the evaluation of competitors for their ability to solve given biological problems using the following skills: In the IBO tasks the names of organisms will be the national names (no description) together with the scientific names (Latin) in bracket ...

PDF

... distribution. In such instances, poor approximations may result. Next, the data and experimental procedures are outline. Data and Procedure To evaluate this framework, 10 replications were completed, each consisting of 25 observations of pseudo-random data for Y, X and e, and a vector of coefficient ...

... distribution. In such instances, poor approximations may result. Next, the data and experimental procedures are outline. Data and Procedure To evaluate this framework, 10 replications were completed, each consisting of 25 observations of pseudo-random data for Y, X and e, and a vector of coefficient ...

Robust and scalable multiphysics solvers for unfitted finite element

... Embedded boundary methods are very attractive, because eliminate the need to define bodyfitted meshes. In particular, at large scales, the meshing step is a bottleneck of the simulation pipeline, since mesh generators do not usually scale properly. In some other situations, like in additive manufact ...

... Embedded boundary methods are very attractive, because eliminate the need to define bodyfitted meshes. In particular, at large scales, the meshing step is a bottleneck of the simulation pipeline, since mesh generators do not usually scale properly. In some other situations, like in additive manufact ...

# Monte Carlo method

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other mathematical methods. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution.In physics-related problems, Monte Carlo methods are quite 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). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk in business and, in math, evaluation of multidimensional definite integrals with complicated boundary conditions. In application to space and oil exploration problems, Monte Carlo–based predictions of failure, cost overruns and schedule overruns are routinely better than human intuition or alternative ""soft"" methods.In principle, Monte Carlo methods can be used to solve any problem having a probabilistic interpretation. By the law of large numbers, integrals described by the expected value of some random variable can be approximated by taking the empirical mean (a.k.a. the sample mean) of independent samples of the variable. When the probability distribution of the variable is too complex, we often use a Markov Chain Monte Carlo (MCMC) sampler. The central idea is to design a judicious Markov chain model with a prescribed stationary probability distribution. By the ergodic theorem, the stationary probability distribution is approximated by the empirical measures of the random states of the MCMC sampler.In other important problems we are interested in generating draws from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability distributions can always be interpreted as the distributions of the random states of a Markov process whose transition probabilities depends on the distributions of the current random states (see McKean-Vlasov processes, nonlinear filtering equation). In other instances we are given a flow of probability distributions with an increasing level of sampling complexity (path spaces models with an increasing time horizon, Boltzmann-Gibbs measures associated with decreasing temperature parameters, and many others). These models can also be seen as the evolution of the law of the random states of a nonlinear Markov chain. A natural way to simulate these sophisticated nonlinear Markov processes is to sample a large number of copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures. In contrast with traditional Monte Carlo and Markov chain Monte Carlo methodologies these mean field particle techniques rely on sequential interacting samples. The terminology mean field reflects the fact that each of the samples (a.k.a. particles, individuals, walkers, agents, creatures, or phenotypes) interacts with the empirical measures of the process. When the size of the system tends to infinity, these random empirical measures converge to the deterministic distribution of the random states of the nonlinear Markov chain, so that the statistical interaction between particles vanishes.