Markov chain Monte Carlo simulation

Berg, B.A. Markov Chain Monte Carlo Simulations and Their Statistical Analysis, World Scientific,... 

Lyons M, Yang RSH, Mayeno AN, Reisfeld B. 2008. Computational toxicology of chloroform reverse dosimetry using Bayesian inference, Markov chain Monte Carlo simulation, and human biomonitoring data. Environ Health Perspect 116 1040-1046. 

B. A. Berg (2003) Multicanonical simulations step by step. Comp. Phys. Comm. 153, pp. 397-406 ibid. (2004) Markov Chain Monte Carlo Simulations and their Statistical Analysis. World Scientific P. 380... 

Fuzzy simulation approach analyses Markov Chain Monte Carlo simulations... 

A true PPC requires sampling from the posterior distribution of the fixed and random effects in the model, which is typically not known. A complete solution then usually requires Markov Chain Monte Carlo simulation, which is not easy to implement. Luckily for the analyst, Yano, Sheiner, and Beal (2001) showed that complete implementation of the algorithm does not appear to be necessary since fixing the values of the model parameters to their final values obtained using maximum likelihood resulted in PPC distributions that were as good as the full-blown Bayesian PPC distributions. In other words, using a predictive check resulted in distributions that were similar to PPC distributions. Unfortunately they also showed that the PPC is very conservative and not very powerful at detecting model misspecification. 

Keywords Bayes theorem conditional probability information entropy Kalman Filter Markov Chain Monte Carlo simulation model identifiability particulate matter regression problem reliability structural health monitoring... 

Adaptive Markov Chain Monte Carlo Simulation 2.5.3.1 Metropolis-Hastings Algorithm... 

Keywords asymptotic expansion evidence information entropy Markov Chain Monte Carlo simulation modal identification Ockham factor regression problem robustness seismic attenuation... 

Beck, J. L. and Au, S. K. Bayesian updating of structural models and reliability using Markov Chain Monte Carlo simulation. Journal of Engineering Mechanics (ASCE) 128(4) (2002), 380-391. 

Figure 1. Illustration of the SS procedure a) Conditional level 0 Standard Monte Carlo simulation b) Conditional level 0 adaptive selection of yi c) Conditional level 1 Markov Chain Monte Carlo simulation d) Conditional level 1 adaptive selection ofy2-...

Parameterization is seen as calibration of the simulator. Sampling from the posterior of parameters is made using Markov Chain Monte Carlo simulation. The sample can be used directly in the Monte Carlo simulation. Here we ran OpenBUGS (Lunn et al., 2009) from R (R Development Core Team, 2008), which makes it possible to parameterize the model and run the simulator in the R environment. 

R functions for performing the Bayesian analysis and Markov chain Monte Carlo simulations shown in this text are included on a website maintained for this text. The functions written for this book have been put into an R package (or library if you re unfamiliar with R) called Bolstad2. The latest version of the package can always be found on CRAN, and for all platforms (Windows, Mac, Linux). This package should not be confused with the Bol stad package, which contains a wholly different set of functions described in Bolstad (2007). 

B. A. Berg, Markov Chain Monte Carlo Simulations (Singapore World Scientific, 2004). 

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