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Christian P. Robert, Mar 14, 2014 Available from:### Click to see the full-text of:

Article: Introducing Monte Carlo Methods with R

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##### Chapter: Classification and Data Mining

01/2012: chapter A Continuous Time Mover-Stayer Model for Labor Market in a Northern Italian Area: pages 101-110; Springer., ISBN: 9783642288937 - [Show abstract] [Hide abstract]

**ABSTRACT:**Frequently a researcher is interested in a theoretical distribution or characteristics of that distribution, such as its mean, standard deviation, or 2.5 and 97.5 percentiles. One hundred or even 50 years ago, we were restricted practically by computing limitations to theoretical distributions that are described by an explicit equation, such as the binomial or multivariate normal distribution. Using mathematical models of distributions often requires considerable mathematical ability, and also imposes rather severe and often intractable assumptions on the applied researchers (e.g., normality, independence, variance assumptions, and so on). But computer simulations now provide more flexibility specifying distributions, which in turn provide more flexibility specifying models. One contemporary simulation technique is Markov chain Monte Carlo (MCMC) simulation, which can specify arbitrarily complex and nested multivariate distributions. It can even combine different theoretical families of variates. Another contemporary technique is the bootstrap, which can construct sampling distributions of conventional statistics that are free from most (but not all) assumptions. It can even create sampling distributions for new or exotic test statistics that the researcher created for a specific experimentAPA handbook of research methods in psychology, Edited by Cooper, Harris (Ed); Camic, Paul M. (Ed); Long, Debra L. (Ed); Panter, A. T. (Ed); Rindskopf, David (Ed); Sher, Kenneth J. (Ed, 01/2012: chapter Bootstrapping and Monte Carlo methods.: pages 407-425; American Psychological Association. -
##### Article: The Metropolis—Hastings Algorithm

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**ABSTRACT:**This chapter is the first of a series on simulation methods based on Markov chains. However, it is a somewhat strange introduction because it contains a description of the most general algorithm of all. The next chapter (Chapter 8) concentrates on the more specific slice sampler, which then introduces the Gibbs sampler (Chapters 9 and 10), which, in turn, is a special case of the Metropolis–Hastings algorithm. (However, the Gibbs sampler is different in both fundamental methodology and historical motivation.)