# Questions tagged [hierarchical-bayesian]

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

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### Bayesian Hierarchical Clustering prior update

I am working through Heller and Ghahramani's "Bayesian Hierarchical Clustering" paper (https://www2.stat.duke.edu/~kheller/bhc.pdf) and things aren't quite working out the way I expect with ...
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### Posterior Distribution in a Bayesian Multivariate Normal Model

I am currently working on a Bayesian inference problem and would appreciate some help on computing the posterior distribution of a hyperparameter within a specific multivariate normal model. Below, I ...
1 vote
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### Bayesian hypothesis testing using posterior samples of estimated parameter

I'm modeling recruitment curves using a Hierarchical Bayesian model. There is a key parameter in my recruitment curve, let's call it $P$. I have two groups (A and B) of participants of respective size ...
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### Difficulties with estimation and strange fitted values for BVAR (BVAR R package)

I'm using the BVAR package in R to estimate a Bayesian vector autoregression involving the following monthly variables: US Capacity utilization, US Total Employees, US PCE index, and 5,10,20,30 year ...
1 vote
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### Determining the number of interactions between the independent variables

I am trying to use GLMMs models to analysis the morbidity status of child (yes or no) with mother’s demographic and environmental factors like Wealth with factors ("Lower quartiles”,"...
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### The "Multiple Error Terms" notation for hierarchical models

I'm seeking clarification regarding notation for Bayesian hierarchical models, specifically the mixed effects model. Consider the following hierarchical model for the outcome of unit $i \in N$ in ...
1 vote
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### How can a Bayesian linear hierarchical random intercept model with normally distributed priors for coefficients represent a non-normally DV?

Suppose you have a hierarchical random intercept model with a dependent variable that is zero inflated. The link function is linear and the priors for the coefficients are normally distributed. In ...
1 vote
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### Does a variance decomposition make sense with a non-linear link function?

I am doing a variance decomposition, with a hierarchal random intercept model like the one below (BRMS R Code): ...
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### Alternatives to spatial and temporal aggregation of time series to discover more learnable patterns

Given taxi demand time series of towns in a country. I would like to do demand forecasting. I noticed that when the town's time series is zero inflated the prediction is poor. However, when these ...
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### Using Bayesian statistics in time series forecasting

I would like to forecast demand count time series of taxi fleets at different locations on the map at different points in time. I.e. multivariate demand Time series forecasting. Given hierarchinal ...
1 vote
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### Bayesian hierarchical exchangeability assumptions reasonable with a check treatment?

This is information I believe to be true A practical feature of hierarchical Bayesian models is that partial pooling reduces (eliminates?) the need of adjusting for multiple comparisons when ...
1 vote
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### Proper analysis of completely crossed design with subjects and items as random effects (brms)

I have the following study design: stimuli: 240 pictures: 6 pictures of 40 students each (each student fixated one of six points and during each fixation one picture was taken) each stimulus was ...
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1 vote
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### In Bayesian modelling how to interpret hierarchical hyperparameters with regards to "borrowing"?

With regards to hierarchical models I often see these referred to as groups borrowing information from each other e.g. It will be seen that the hierarchical model posterior estimates for one school ...
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### Bayesian meta-analysis: Why and how to weight individual study's contribution to overall effect?

I'm interested in performing a Bayesian meta-analysis, specifically, using a random-effects hierarchical model (as described here). Briefly, in this model we assume that the $k$th study's reported (...
37 views

### How multilevel Bayesian models handle group imbalance

I’ve read that partial pooling (multilevel / hierarchical models) can balance the extremes: on one hand, zero pooling where every group receives its own parameters, non influenced by other groups. And ...
1 vote
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### Bayesian Hierarchical Regression Models for Panel Data

I am fairly comfortable with Bayesian hierarchical regression models, but I am new to panel data analysis. As someone from the social sciences, I have found that the majority of resources on panel ...
223 views

### brms model specification with 3 (crossed or nested?) levels

I have a data set that looks like this toy data ...
39 views

### Conditionally conjugate prior for non-nested (i.e. crossed) normal model?

I am trying to write/understand a conditionally-conjugate Gibbs sampler for what is essentially a linear, mixed effects model. I more or less get the conditionally-conjugate posterior for the ...
25 views

### Is there a way to demonstrate strength of a Hierarchical Bayesian Model versus a non-Hierarchical Bayesian Model on simulated data?

Is there a way to demonstrate strength of a Hierarchical Bayesian Model versus a non-Hierarchical Bayesian Model on simulated data? I'm ideally looking for a plot that shows that a Hierarchical ...
1 vote
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### Nonconvergence of some parameters in MCMC of Hierarchical Bayesian Model

In short: MCMC is used to construct posterior distributions for parameters of central tendency and all parameters used in the formula for this central tendency. I only care about the parameters of ...
41 views

### Why don't we typically drop a category as a baseline in Bayesian hierarchical linear regression?

Let's say we have two categorical variables the first with categories $j = 1,..., J$ and the other with categories $k = 1,...,K$. Often in Bayesian hierarchical linear regression, we might have a ...
45 views

### Post-hoc identifiability for Bayesian multilevel regression model

In , Ogle & Barber discuss a method for ensuring identifiability of certain Bayesian multilevel regression models; they call this method "post-sweeping". I have a couple of related ...
55 views

### Statistcially assessing how similar curves are?

I have intensity curves (~9 reps) of bacterial fluorescence over 2.2 cm from 4 groups (A, B, C and D unknown) and three treatments (10 mM, 1 mM and 0 mM). My current code is below. I wish to show how ...
63 views

### Multilevel (Hierarchical) Bayesian Model in R

I have my dataset with different mutations as unit of analysis. These mutations belong to 5 different classes. Also, I have collected, 9 features about these mutations. In other words I have 12 ...
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### LOOCV comparison partially polled vs unpooled model

When using the leave-one-out cross-validation (LOOCV) as a metric, is the unpooled Bayesian model bound to outperform the partially pooled Bayesian model?
62 views

### Dropping a hierarchical linear model intercept when centering the outcome at 0?

Suppose a hierarchical linear model with "random intercepts" $\mu_i$ fit to some raw (unscaled) data: $$y_i \sim N(\mu_0 + \mu_i, \sigma) \\ \mu_i \sim N(0,\sigma)$$ If I rescale $y_i$ by ...
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### How do I interpret the slope of a random slope model?

I am trying to use a Bayesian random slope model to determine whether the hierarchical structure of the data is biasing my results. I am investigating the effect of IQ on test scores. I have three ...
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### Method for type S error control with small number of testings?

I have gone through Gelman's paper http://www.stat.columbia.edu/~gelman/research/published/francis8.pdf. It covers a Bayesian testing procedure for hierarchical models. $Q:$ Is this procedure ...
It's known that integrating out $\Lambda \equiv \Sigma^{-1}$ below, $$y|\Lambda \sim \mathcal N(0, \Lambda^{-1}),$$ $$\Lambda \sim \mathcal W(M^{-1}, \nu)$$ leads to a multivariate t distribution ...