# Questions tagged [hierarchical-bayesian]

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

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### Attempting to compare Bayesian and Frequentist mixed effects models

This question may be better suited for stack overflow (happy to move it if deemed too off topic). I am currently in the process of learning Bayesian analysis using stan in R as my software. ...
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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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### Bayesian inference on mean of statistic from population

Suppose that a collection of time intervals $t_i$ have occurred, for $i=1,...,n$. These should be considered as samples from a population governed by some distribution. During these time intervals, ...
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### Specification of priors for multivariet hierarchical regression using MCMCglmm

I'm analyzing data from experiment, where people had to select a point in plane. I'm trying to asses which atributes of the task and personality are asociated with the outcome. Becouse we used ...
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### What distributions might describe the percentage of a population with a trait across groups?

Suppose I have a large number of urns, each with a different ratio $r$ of white and black balls. Some urns may be full of white balls or full of black balls. What kinds of distributions or processes ...
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### Bayes Rule with Model Comparison

In Doing Bayesian Data Analysis 2ed, by Kruschke, in chapter 10, we get two equations (10.1, 10.2) for which no hint as to how they are obtained is given... How does one get the second equality in ...
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### Ergodicity of MCMC in a hierarchical model

Many of the Bayesian hierarchical models that I am studying use a Markov chain as the model. These hierarchical models use different MCMC techniques to sample low-level and high-level parameters. My ...
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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, \begin{equation}\label{eq:...
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### learning a gaussian distribution through dependent vairiable observations

Is it possible to infer the parameters of a gaussian random variable by sampling from a distribution that is linearly dependent on the variable of interest? For example: y = Ax + n With x ~ N(u,S) ...
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### Gaussian Latent Variable Parameter Learning

Do any approximate (preferably message passing type) inference algorithms exist for learning the parameters of a latent Gaussian variable (from information of other dependent observed variables)? ...
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### Bayesian output vs frequentist. Which should I rely on? MLM/ RE HLM

I have 2 questions. 1)My Bayesian output is providing some trouble. I have data that will vary across 5 countries. This means my group level has a small n of 5. This results in my data hovering ...
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### What models predict higher levels of hierchical structure?

The wikipedia page for multilevel model states: The dependent variable must be examined at the lowest level of analysis. I am interested in predicting measures at higher levels of analysis. In ...
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### In Bayesian statistics, what do mu, eta, and tau tend to represent?

In the eight schools example from Gelman, he sets his parameters as mu, eta, and tau. ...
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### Meaning of Baseline Before Sum to Zero

I am trying to specify a Bayesian hierarchical split-plot model in JAGS. I have been following Doing Bayesian Data Analysis by John K. Kruschke, however the model I am attempting is not included in ...
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### Comparing top level group effects using a 3-level hierarchical regression

I would like to detect group effects (if any) along with statistical confidences. I have a hierarchical data set structured as follows: Drug Groups ...
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### Variational Bayes for Multivariate Normal distributed data with shared mean and precision

I have a model represented in graphical model and part of this model states that there are N data points that are generated from multivariate normal with shared mean vector and covariance/precision ...
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### Meaning of Intercept Parameter in a Bayesian Longitudinal HLM

I have been working through John Kruschke's excellent book on Bayesian Data Analysis but now have found myself in experimental-design territory not covered in the book: a longitudinal linear mixed-...
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### What is the correct form of Metropolis Hasting step in scaled Inverse Wishart prior for covariance matrix?

I was going through the paper of O'Malley and Zaslavsky (2008) for the scaled inverse Wishart priors for a covariance matrix, in order to write an R-code for hierarchical Bayesian estimation of mixed ...
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### Multilevel modelling of effects for positive values: Which distributions to use

I am currently trying to figure out what would be the best way to model a bayesian hierarchical regression for data, where the criterion value can only be positive and I am assume that the effects are ...
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### How to put a prior on parameter “x” instead of parameter “y” if x and y are related

Background: I'm new to the Bayesian approach and thus am trying to better understand the multi-level (i.e., hierarchical) nature of the Bayesian approach. Question: Suppose I have a parameter ...