Questions tagged [hierarchical-bayesian]

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

226 questions
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Horseshoe priors and random slope/intercept regressions

I'm interested in using the horseshoe prior (or the related hierarchical-shrinkage family of priors) for regression coefficients of a traditional multilevel regression (e.g., random slopes/intercepts)....
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Why does increasing number of observations in linear mixed model cause Bayesian modelling approach to fail?

I have a fairly good understanding of the theory behind Bayesian modeling and I have started to attempt some practical modeling using jags in R. I have been ...
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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 ...
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Gibbs sampling deriving complete conditionals with mixture priors

My question is about the derivation of the complete conditionals for Gibbs sampling in a hierarchical model where some of the parameters are mixtures of point-masses and Normal distributions. The ...
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Hierarchical model: question on frequentist estimation

I am interested in understanding the differences between Bayesian and Frequentist estimation in the context of hierarchical models. Consider $n$ subjects, where for subject $i$ there are $k_i$ ...
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How to infer a prior belief after observing a behavior

My participant goes through a maze made of 32 T intersections. At each intersection he must choose whether to go either to the left or to the right: one option will lead to another T intersection, ...
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Likelihood function of a hierarchical model

I have the following model: $$y\sim\textrm{MvNormal}\left(\mu,\Sigma\right)\\ p=\textrm{logistic}\left(y\right)\\ k\sim\textrm{Binomial}\left(p,n\right)$$ Where $\mu$ and $\Sigma$ are free ...
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Run MAP estimates before MCMC in most cases?

I am learning Bayesian statistics. I found that this pymc3 introduction sometimes uses MAP to estimate the parameters for the MCMC input (the regression example), but the intro doesn't run MAP for ...
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Implementing a hierarchical bayesian graphical model in R

The shorter version: 1. Bayesian graphical models are new to me. 2. I want to use R to model spatial variation in county level crime using a BGN. I have been working with bnlearn, and would ideally ...
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Difference between hierarchical Bayes and random parameter/effects models?

From my limited understanding, the difference is mainly that hierarchical Bayes (HB) incorporates parameter distribution priors that will "constrain" the individual parameters to one side of the ...
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Effect size for contrasts in hierarchical Bayesian “ANOVA”

Kruschke (2014) shows in his book how to compute posterior distributions of effect sizes (standardized mean difference) for the Bayesian analogues of frequentist independent-samples t-tests, and one-...
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What convergence diagnostics are appropriate for a Bayesian hierarchical logistic regression model?

Using WinBUGS, I fit several Bayesian hierarchical logistic regression models for the mean of a binary response variable conditional on a set of criteria. I am now using CODA in R to determine if my ...
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In a Hierarchical Bayesian Model, how can we sample and see how a prior distribution looks like if it contains hyperparameters with hyperpriors?

I have a Bayesian Hierarchical Model that looks like: Y_i \sim N(\mu, \sigma^2) \\ \mu \sim N(\mu_0, \sigma_0^2) \\ \sigma^2 \sim Gamma(1,1) \\ \mu_0 \sim N(0,1) \\ \sigma_0^2 \sim ...
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Can Bayesian Optimization solve this problem?

Suppose ${\bf{x}} = (x_1,\ldots,x_n)$ and $f({\bf{x}})\propto 1_A({\bf{x}}) \prod_{i=1}^n {x_i}^{\alpha_i-1} e^{-\beta_i x_i}$ , i.e. $f$ is proportional to the product of independent gamma ...
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How to do classification in mixed effect models in python. My data is nested into groups with binary outcome

Lets say I have 10 sellers (S1-S10). Each seller has 7 buyers which are different for each seller (B1-B7 for S1, B11-B17 for S2 and so on). Each Seller buyer combination has a product category (P1, P2....
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Appropriate Distribution for Diagonal Covariance Matrices

Let's say I have a model like: \begin{align} X\mid\mu,\Sigma_X &\sim \mathcal{N}(\mu,\Sigma_X)\\ \mu\mid m, \Sigma_\mu &\sim \mathcal{N}(m,\Sigma_\mu) \\ \Sigma_X\mid \Psi, c &\sim \...
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Hierarchical Black Box Variational Inference : Choice of inverse flow

I am reading through Black Box Variational Inference, and having trouble understanding the section for hierarchical inference, where the normalizing flow is introduced. Should this be an arbitrary ...
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Hierarchical Linear Regression should always outperform Ordinary Linear Regression

I am building a hierarchical linear model with varying intercepts. It takes the form for each unit $i$ in group $j$: $$y_{ij} = \alpha_j + \beta_1 x_{ij,1} + \beta_2 x_{ij,2} \quad (1)$$ I am ...
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How to fit newer cohorts using Pareto/NBD or Beta/Geo for CLTV

I am trying to fit the popular Pareto/NBD or Beta/Geometric models for non-contractual, continuous customer data. On top of that I then fit the Gamma/Gamma model for monetary value (using the very ...
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Applications of Hierarchical Dirichlet Process to Continuous Data

I read Yee Whye Teh et al.'s paper on Hierarchical Dirichlet Process. In section 5, they show sampling algorithm using base distribution H and data distribution F. One of their applications is HDP-...
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How to predict using Spatial temporal hierarchical bayesian models

I am using the R package CARBayesST to fit a Spatial-temporal Bayesian models. I want to use piece-wise ST model proposed by Lee and Lawson, 2017. The package does not have a built-in predict ...
216 views

Formulating a hierarchical Bayesian model for gambling (Pymc3)

I am quite new to Bayesian modeling and trying to wrap my head around how to choose hyperpriors and formulate the model. I am using Pymc3 My example data is gambling related. People play a 'balloon' ...
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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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Gibbs sampling in the Hierarchical Dirichlet Process

For an inference problem using a Dirichlet Process prior, one can derive a "basic" Gibbs sampling scheme, where we have a conditional for any parameter $\theta_i$ given the samples $x_i$ and all the ...
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Implementing a hierarchical bayesian model with latent independent and dependent variables for spatial analysis (in stan)

I am moderately familiar with frequentist hierarchical modeling, structural equation modeling, and hierarchical structural equation modeling. I am also moderately familiar with bayesian graphical ...
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I am implementing a Bayesian Mixed Effects model in my research problem. The model is written as, $y_i = X_i(\alpha + \beta_i) + \epsilon_i$, where $i = 1, 2, \ldots, m$ is the index of response, $j = ... 0answers 504 views Issue with Categorical distribution in hierarchical modeling with PYMC I am trying to implement a "hierarchical" model in PYMC in which the membership of observations to groups is not static (similar to the latent assignment of words to topics in Latent Dirichlet ... 0answers 97 views If all components of a hierarchical model have not converged, can we say that any parameters have truly converged? I'm working with a hierarchical regression model of the following form similar to that presented in Peter D. Hoff's book, A First Course in Bayesian Statistical Methods:$\boldsymbol{Y}_j \sim \text{...
$\newcommand{\N}{\operatorname{N}}$$\newcommand{\IG}{\operatorname{IG}}$My understanding of bayesian random effects (I understand that this concept is a frequentist one, but I use it for simplicity) ...