# Questions tagged [hierarchical-bayesian]

Hierarchical Bayesian models specify priors on parameters and hyperpriors on the parameters of the prior distributions

420 questions
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### XKCD's modified Bayes theorem: actually kinda reasonable?

I know this is from a comic famous for taking advantage of certain analytical tendencies, but it actually looks kind of reasonable after a few minutes of staring. Can anyone outline for me what this "...
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### What's the difference between “deep learning” and multilevel/hierarchical modeling?

Is "deep learning" just another term for multilevel/hierarchical modeling? I'm much more familiar with the latter than the former, but from what I can tell, the primary difference is not in their ...
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### What is the problem with empirical priors?

In literature I sometimes stumple upon the remark, that choosing priors that depend on the data itself (for example Zellners g-prior) can be criticized from a theoretical point of view. Where exactly ...
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### In Gelman's 8 school example, why is the standard error of the individual estimate assumed known?

Context: In Gelman's 8-school example (Bayesian Data Analysis, 3rd edition, Ch 5.5) there are eight parallel experiments in 8 schools testing the effect of coaching. Each experiment yields an ...
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### What prior distributions could/should be used for the variance in a hierarchical bayesisan model when the mean variance is of interest?

In his widely cited paper Prior distributions for variance parameters in hierarchical models (916 citation so far on Google Scholar) Gelman proposes that good non-informative prior distributions for ...
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### Bayesian estimation of $N$ of a binomial distribution

This question is a technical follow-up of this question. I have trouble understanding and replicating the model presented in Raftery (1988): Inference for the binomial $N$ parameter: a hierarchical ...
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### Why does adding a lag effect increase mean deviance in a Bayesian hierarchical model?

Background: I'm currently doing some work comparing various Bayesian hierarchical models. The data $y_{ij}$ are numeric measures of well-being for participant $i$ and time $j$. I have around 1000 ...
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### Why does the redundant mean parameterization speed up Gibbs MCMC?

In Gelman & Hill (2007)'s book (Data Analysis Using Regression and Multilevel/Hierarchical Models), the authors claim that including redundant mean parameters can help speed up MCMC. The given ...
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### What precisely does it mean to borrow information?

I often people them talk about information borrowing or information sharing in Bayesian hierarchical models. I can't seem to get a straight answer about what this actually means and if it is unique to ...
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### What are the parameters of a Wishart-Wishart posterior?

When infering the precision matrix $\boldsymbol{\Lambda}$ of a normal distribution used to generate $N$ D-dimensional vectors $\mathbf{x_1},..,\mathbf{x_N}$ \begin{align} \mathbf{x_i} &\sim \...
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### Hyperprior density for hierarchical Gamma-Poisson model

In a hierarchical model of data $y$ where $$y \sim \textrm{Poisson}(\lambda)$$ $$\lambda \sim \textrm{Gamma}(\alpha, \beta)$$ it appears to be typical in practice to chose values ($\alpha, \beta)$ ...
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### Multinomial-Dirichlet model with hyperprior distribution on the concentration parameters

I will try to describe the problem at hand as general as possible. I am modeling observations as a categorical distribution with a parameter probability vector theta. Then, I assume the parameter ...
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### What is a good analogy to illustrate the strengths of Hierarchical Bayesian Models?

I'm relatively new to bayesian statistics and have been using JAGS recently to build hierarchical bayesian models on different datasets. While I'm very satisfied of the results (compared to standard ...
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### Why does Restricted maximum likelihood yield a better (unbiased) estimate of the variance?

I'm reading Doug Bates' theory paper on R's lme4 package to better understand the nitty-gritty of mixed models, and came across an intriguing result that I'd like to understand better, about using ...
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### Normalizing constant irrelevant in Bayes theorem?

I've been reviewing Bayesian literature in an attempt to utilize Bayesian inference for hypothesis testing when I have very well established priors, but there's one thing I cannot get my head around: ...