# Questions tagged [hierarchical-bayesian]

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

433 questions
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### Question about foundations of the uniform shrinkage prior

I am collecting papers about the uniform shrinkage prior for hierarchical Bayesian model. In "A prior for the variance in hierarchical models" of Michael J. Daniels it is stated at the end of page two ...
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### How do I incorporate personalization to a Bayesian ranking engine?

I'm looking to quickly get smart on how to add personalization into a Bayesian-based recommendation system. I'm using clickstream data and Bayesian statistics to estimate probabilities of purchase ...
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### How can posterior be persisted and reconstituted as future prior?

Suppose I model a data generating process as a hierarchal model and have made some training observation from the process. To learn about the process, with the observations I run the bayesian ...
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### Replicate simulation study from a paper and calculate the MSE in R

I have implemented a Gibbs Sampler for the Bayesian Elastic Net (BEN) according to this paper on Penalized Regression by Kyung et al. In this paper, they execute a simulation study that has been used ...
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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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### priors for strictly positive index or score types of variables

Is there a prior that's commonly used for "index" or "score" type variables that are user-defined as a weighted sum of a small number of variables (sometimes with pre-defined interaction contributions)...
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### Bayesian inference and degrees of freedom

While learning frequentist linear regressions, one thing the professors always talked about was about the number of degrees of freedom, I never saw this expression in a bayesian book though. Perhaps ...
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### Parameters for a Hierarchical Multinomial Regression

I am trying to fit a hierarchical multinomial regression to cross sectional data. I have around 2000 units with only one observation per unit. I have a binomial response variable and 14 dummy ...
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### A better bayesian way of modelling autoregressive mixtures

I have a JAGS hierarchical model which includes a temporal sub-model for the primary vote share between four party groups (LNP, Labor, Green, and Other). For each day in the temporal model, the vote ...
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### Selecting a Bayes shrinkage prior

I'm looking for a way to integrate prior knowledge about a parameter in a context equivalent to Bayesian hierarchical models. I come from frequentist background and I'm uninitiated in hierarchical ...
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### Jeffrey's prior for variance

I'm dealing with hierarchical model where $Y_i$ are from normal distribution. About variance the formulation is the following: Similarly, the data contain substantial information about the measurement ...
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### How to do Empirical Bayes Estimation of HLM parameteres in R?

I am modelling the impacts on students' achievemens using HLM (2 levels only), with the lme4 package in R. I would like now to estimate the Empirical Bayes Estimates and the Empirical Bayes Grand ...
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### Mixture model as a prior distribution

I've just started working with Bayesian models. My question is in the context of hierarchical Bayesian model. Suppose you have n models to train. However, some of these models are similar to each ...
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### Update rule for beta distribution with fixed K/confidence/sample size

Normally you have a beta distribution with shape parameters $a$ and $b$. The mean of this distribution is $a / (a + b)$ and the sample size, or the confidence (or K) is $a + b$. Now, if you do some ...
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### Sequential Monte Carlo for hierarchical models

Does anybody know, can Sequential Monte Carlo be applied for multi-dimensional problems i.e. simulating more than 1 distribution like in hierarchical models? Maybe you know some following literature
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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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### Non-converging coefficients in hierarchial Bayes analysis of discrete choice

I am trying to analyse repeated responses from a discrete choice experiment. The DCE had one continuous parameter and five 3-level categorical parameters. I started with a multinomial logit and the ...
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### Is there any reason to prefer a bayesian model with few variables?

I have two alternative hierachical bayesian models that were designed to the describe the same process (from a high-level point-of-view). Both model provides comparable (but not identical) inferences ...
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### How to derive the conditional posterior density in hierarchical bayesian models?

I was reading on Gelman's Bayesian Data Analysis - Chapter 5 - Hierarchical model Suppose: data : $y_j$ s parameter: $\theta$ hyperparameter: $\phi$ On page 126, he mentions the analytical ...
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### Flipping random coins from a bag - equivalent to a single coin?

My first and I think naive question here. I am trying to model a certain business, and the simplest model I am willing to test is: 1. there is a bag of differently biased coins. 2. every step, a ...
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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 ...
671 views

### What level to use when comparing subjects in a hierarchical Bayesian analysis?

Say that I have an experiment where I test the reaction time of a number of subjects where each subject makes many reaction time trials. In a Bayesian framework the reaction times ($y$) could be ...
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### Hierarchical models for multiple comparisons - multiple outcomes context

I've just been (re-)reading Gelman's Why we (usually) don't have to worry about multiple comparisons. In particular the section "Multiple outcomes and other challenges" mentions using a hierarchical ...
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### Computing a marginal posterior of a hierarchical model

This is my first time posting an actual homework question. Usually I have more local resources such as office hours and student peers but this time I am a little short on those. I also need to rest ...