Questions tagged [hierarchical-bayesian]

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

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Crossvalidation in hierarchical bayesian models (HBMs)

I am trying to find a way to cross-validate Hierarchical Bayesian Models used for predicting and modelling abundance in Species Distribution Models. For this purpose, I have tried posterior predictive ...
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Run MAP estimates before MCMC in most cases?

I am learning Bayesian statistics. I found that this pymc3 introduction sometimes uses MAP to estimate the parameters for the MCMC input (the regression example), but the intro doesn't run MAP for ...
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Are predictive distributions supposed to be distributions of future data?

In frequentist analysis, we define a 95% prediction interval as an interval that will contain the next observation 95% of the time under repeated sampling of the entire experiment and prediction. If ...
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Seeking a closed form for a posterior distribution

In the book Bayesian Data Analysis by Gelman et al. (3rd edition, 2014), a hierarchical model (or one-way random-effects ANOVA) is presented in section 5.4 as follows, \label{eq:...
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Probability distribution to represent group mean of multiple beta distributions

Say I have two coins from a particular mint in the US. I flip coin one 20 times and receive 4 heads, giving me a beta distribution for the bias of coin one of $Beta$($\alpha$=5, $\beta$=17). I then ...
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Gibbs sampling deriving complete conditionals with mixture priors

My question is about the derivation of the complete conditionals for Gibbs sampling in a hierarchical model where some of the parameters are mixtures of point-masses and Normal distributions. The ...
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Hierarchical model: question on frequentist estimation

I am interested in understanding the differences between Bayesian and Frequentist estimation in the context of hierarchical models. Consider $n$ subjects, where for subject $i$ there are $k_i$ ...
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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: ...
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Mixed Effects, Doctors & Operations: predicting on new data containing previously unobserved levels, and updating our confidence accordingly

Here's a quick sketch of a hypothetical situation. There are Doctors $\{1, \ldots, J\}$ who perform different types of operations $\{1, \ldots, K\}$. Our response variable is whether the operation ...
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What are some statistical tests for exchangeability of a data set?

The representation theorem of de Finetti is seen by some as motivation for the use of Bayesian and/or hierarchical modeling. In some settings, it may be plausible to assume measurements are ...
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