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📚 Statistical Inference for Everyone
Chapters ▾
1 Introduction to Probability2 Applications of Probability3 Random Sequences and Visualization4 Introduction to Model Comparison5 Applications of Model Comparison6 Introduction to Parameter Estimation7 Priors, Likelihoods, and Posteriors8 Common Statistical Significance Tests9 Applications of Parameter Estimation and Inference10 Multi-parameter Models11 Introduction to MCMC12 Concluding Thoughts13 Appendix A: Computational Analysis14 Appendix B: Notation and Standards15 Appendix C: Common Distributions and Their Properties16 Appendix D: Tables

Chapter 11: Introduction to MCMC

Once the problems get to a sufficient complexity, the analytical tools and approximations we have employed in previous chapters will no longer work well. In those cases, we turn to simulation techniques, one of which is Markov Chain Monte Carlo (MCMC). It is well beyond this book to talk about the details of this process, but the basic process is the following.

We start with a model of the system, such as the bent coin model in Section 6.4. In that system, we try to estimate the probability that a particular doing will flip heads, quantified by the parameter θ which can take on values from θ=0 (i.e. a coin which only flips tails) through θ=0.5 (i.e. a “fair” coin which flips tails and heads equally) up to θ=1 (i.e. a coin which only flips heads). Our data consists of a total number of flips, N, and how many are heads, h. Although this problem can be done analytically, it is instructive to walk through the solved problem with the new method before looking at more complex models.

MCMC proceeds, roughly, with the following steps

Adapted from Statistical Inference for Everyone, by Brian Blais (Bryant University), licensed under CC BY-SA 4.0 (dual-licensed under the GNU FDL 1.2 or later; this adaptation uses the CC BY-SA grant). Changes were made; this adaptation is distributed under the same license. License: CC-BY-SA-4.0.