The hierarchical Bayes method is one of the most important topics in modern Bayesian analysis. It is a powerful tool for expressing rich statistical models that more fully reflect a given problem than a simpler model could.

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  • The hierarchical Bayes method is one of the most important topics in modern Bayesian analysis. It is a powerful tool for expressing rich statistical models that more fully reflect a given problem than a simpler model could. Given data <math>x\,\! and parameters <math>\vartheta, a simple Bayesian analysis starts with a prior probability (prior) <math>p(\vartheta) and likelihood <math>p(x|\vartheta) to compute a posterior probability <math>p(\vartheta|x) \propto p(x|\vartheta)p(\vartheta). Often the prior on <math>\vartheta depends in turn on other parameters <math>\varphi that are not mentioned in the likelihood. So, the prior <math>p(\vartheta) must be replaced by a prior <math>p(\vartheta|\varphi), and a prior <math>p(\varphi) on the newly introduced parameters <math>\varphi is required, resulting in a posterior probability p(\vartheta,\varphi|x) \propto p(x|\vartheta)p(\vartheta|\varphi)p(\varphi). This is the simplest example of a hierarchical Bayes model. The process may be repeated; for example, the parameters <math>\varphi may depend in turn on additional parameters <math>\psi\,\!, which will require their own prior. Eventually the process must terminate, with priors that do not depend on any other unmentioned parameters.
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  • The hierarchical Bayes method is one of the most important topics in modern Bayesian analysis. It is a powerful tool for expressing rich statistical models that more fully reflect a given problem than a simpler model could.
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  • Hierarchical Bayes model
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