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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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0answers
173 views

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 ...
2
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1answer
106 views

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 ...
2
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1answer
69 views

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 ...
4
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1answer
2k views

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 ...
31
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2answers
10k views

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 ...
2
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0answers
87 views

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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2answers
1k views

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 ...
1
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1answer
384 views

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 ...
3
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0answers
428 views

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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0answers
498 views

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 ...
1
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1answer
1k views

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 ...
2
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0answers
634 views

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 ...
2
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0answers
275 views

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 ...
4
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2answers
1k views

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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1answer
160 views

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
4
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2answers
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: ...
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0answers
395 views

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 ...
2
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1answer
137 views

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 ...
2
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0answers
2k views

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 ...
3
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2answers
289 views

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 ...
2
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1answer
310 views

Decomposing Laplace prior for a hierarchical representation of a model

I have a conditional Laplace prior: $$ \pi(\boldsymbol{\beta}|\sigma^2) = \prod\limits_{j=1}^{p}\frac{\lambda}{2\sqrt{\sigma^2}}e^{-\lambda|\beta_j|/\sqrt{\sigma^2}} $$ and a marginal prior on $\...
2
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0answers
209 views

inverse logistic regression with binary covariates

I am currently using a hierarchical Bayesian framework to investigate a problem with both a single binary response variable and binary covariates, $P(Y=1 | X_i=1), i=1,\ldots,n$. Using R/JAGS I can ...
1
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1answer
201 views

How to make inferences on group SD and and the SD of the group SD in a hierarchical Bayesian model?

The hierarchical model specified below is quite "standard" and easy to implement in for example JAGS/BUGS. It has an hierarchical gamma prior on the subject's precisions ($\tau_j$) which in turn has ...
6
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1answer
3k views

Two-level hierarchical model using time-series cross sectional data?

A question from someone who is fairly new to hierarchical modeling, and I'm looking for the best approach within R, preferably with the package lme4, MCMCpack, or rjags using a BUGS document. I'm ...
7
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2answers
1k views

What level to use when making inferences on the group mean in a hierarchical Bayesian analysis?

(This question is a bit related to a previous question of mine, but that question was about between subject comparison while this question is specifically about making inferences the group mean.) ...
10
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3answers
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 ...
4
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0answers
559 views

Negative number of parameters in hierarchical bayesian model

I'm using Deviance information criterion to assess the fitness in my Bayesian hierarchical model. The functional form of this criterion is as follows: $$DIC=p_{D}+\bar{D}$$ where $p_{D}=\bar{D(\theta)...
16
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2answers
5k views

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 ...
8
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1answer
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 ...
10
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2answers
1k views

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 ...
2
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1answer
125 views

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 ...
2
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0answers
215 views

Reporting contrasts between binary probability parameters in Bayesian data analysis - odds ratios or difference in probability?

In a bayesian data analysis, if one is modeling differences in binomial/bernoulli probability parameter differences between populations, is it still standard to report the difference in the binary ...
8
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1answer
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 ...