Bayesian Hierarchical Modelling (BHM)

Marcel van Oijen ()

Chapter Chapter 16 in Bayesian Compendium, 2020, pp 121-128 from Springer

Abstract: Abstract In the previous chapters, our statistical procedure was very simple: define a prior probability distribution for the parameters $$p[\theta ]$$ and a likelihood function $$L[\theta ]=p[y|\theta ]$$, and that was it. Bayes’ theorem then told us what the posterior distribution would be once we received the data: $$p[\theta |y] \propto p[\theta ] L[\theta ]$$. The prior for the parameter vector was always a fully specified distribution, e.g. the product of known univariate Gaussians. In hierarchical modelling, we do not specify the prior that directly. Instead we make the prior distribution depend on other parameters, which we call hyperparameters.

Date: 2020
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DOI: 10.1007/978-3-030-55897-0_16

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