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Questions tagged [hierarchical-bayesian]

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

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2k views

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: ...
5k views

Covariance matrix proposal distribution

In a MCMC implementation of hierarchical models, with normal random effects and a Wishart prior for their covariance matrix, Gibbs sampling is typically used. However, if we change the distribution ...
378 views

Is rstan or my grid approximation incorrect: deciding between conflicting quantile estimates in Bayesian inference

I have a model to achieve Bayesian estimates the population size $N$ and probability of detection $\theta$ in a binomial distribution solely based on the observed number of observed objects $y$:  p(...
637 views

Hierarchical Bayesian modeling of incidence rates

Kevin Murphy's book discusses a classical Hierarchical Bayesian problem (originally discussed in Johnson and Albert, 1999, p24): Suppose that we are trying to ...
526 views

Relation between Bayesian analysis and Bayesian hierarchical analysis?

I have been studying a Bayesian hierarchical model. In that model all I am dealing is with the estimation of parameters. In Bayesian analysis, loosely speaking, we update our prior knowledge (in light ...
2k views

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 ...
4k views

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 ...
1k views

Bayes-factor for testing a null-hypothesis?

I heard somewhere, that I can directly test (or gather support for) a null-hypothesis using the Bayes-Factor. In my specific experiment, I hypothesize that an experimental manipulation does not have ...
834 views

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 ...
824 views

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 ...
2k views

Hyperprior distributions for the parameters (scale matrix and degrees of freedom) of a wishart prior to an inverse covariance matrix

I'm estimating several inverse covariance matrices of a set of measurements across different subpopulations using an wishart prior in jags/rjags/R. Instead of specifying a scale matrix and degrees ...
690 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 ...
2k views

Hyper-prior for negative binomial in hierarchical model using JAGS/BUGS

Below I'm using a negative binomial because it is more flexible than a simple poisson model. The data are counts $y$ of events for 16 individuals $x$. There are 14 counts (i.e. counting periods) for ...
234 views

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 ...
332 views

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 ...
148 views

418 views

Confusion about Cross-Validation for Hierarchical Bayesian Regression Models

I had two questions regarding model selection for a Hierarchical Bayesian (HB) Regression Model and the purpose of Cross-Validation. 1). I understand cross-validation as one way to perform model ...
244 views

Bayesian Modeling: Yes, No and Maybe Responses

Respondents replied in the following way: Yes: they will be attending No: they won't be attending Maybe: they attach a percentage certainty as an estimate that they'll be attending. E.g. 40% sure ...
319 views

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 ...
668 views

How to find the Likelihood Function in a Bayesian Model given some Data

How should I find the likelihood function of a Bayesian Model? For example, if I'm given a coin, I can use the Bernoulli Distribution as the likelihood function (because I know in advance that the ...
70 views

How to model a multiplicative effect of a parameter

I am having difficulty in fitting a model on data. Basically, I have data about the evaluation of phenotypic property (i.e. hard) of 65 palm trees by 5 judges. As an evaluation scheme, each judge ...
321 views

Why semi/nonparametric models?

Increasing the flexibility of models makes it prone to overfitting. On the other hand, it looks to me that, if the space function classes $\mathcal{F}$ is too big, it is hard to prove bounds on ...
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 ...