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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

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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186 views

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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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 ...
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233 views

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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69 views

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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188 views

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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113 views

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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168 views

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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601 views

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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231 views

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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385 views

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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344 views

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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554 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)...
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117 views

What is the posterior kernel lengthscale of a Gaussian process?

If I have access to multiple samples from a Gaussian process with known covariance kernel but unknown parameters (i.e. unknown lengthscale), it is straightforward to estimate the lengthscale using ...
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307 views

Pro and cons between Bayesian structural time series (BSTS) vs difference-in-differences?

Google's paper markets BSTS's benefits over DID such that "In contrast to classical difference-in-differences schemes, state-space models make it possible to (i) infer the temporal evolution of ...
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110 views

sampling from a posterior derived from hierarchical Bayesian using HMC

I have a complex pdf based on hierarchical Bayesian formalism where x depends on the priors w'and w'', and I consider hyper-prior for the latter's as w=Php(zeta,beta) where Php stands for the hyper ...
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56 views

Dependence between parameters in Bayesian multilevel regression

I am working on a Bayesian multilevel regression model, which is specified as $$ y_{ij}=x_{ij}'\beta+\delta_j+\varepsilon_{ij}\\ \delta_j=\gamma_{\operatorname{region}(j)}+\eta_j $$ where $i$ indexes ...
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77 views

Hierarchical Bayesian Modelling: deriving a Conditional PDF relation

Background I am currently reading through the book: Data Analysis: A Bayesian Tutorial, second edition by D.S. Sivia. I am stumped by one of the relations that he introduces in the context of model ...
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386 views

Hierarchical modelling - partial pooling with correlation

I am doing a Bayesian regression. I have groups of data $(y_1 ~X_1), (y_2~X_2),...$, where each $y$ and $X$ is a vector. The subscript is regarded as group number. The completely unpooled regression ...
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262 views

How to specify the Bayesian version of a clustered-robust standard error OLS in BUGS/JAGS or Stan?

I am trying to reproduce a simple OLS model fitted with clustered-robust standard errors within the Bayesian framework (be it with BUGS/JaGS or with Stan). In R, my frequentist model is the following:...
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29 views

Approaches to fast estimation of new levels of a hierarchical linear model from new data

I have a hierarchical linear model I've applied to a dataset in which the effect of a factor on my outcome measure can vary for different people. Say I have a new individual for whom I have some ...
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255 views

Does a closed form marginal posterior exist for regression coefficients in hierarchical linear model?

Given the standard linear model $$Y=X\beta+\epsilon$$ a Gaussian likelihood function $Y|b,\sigma^2 \sim N(X\beta,\sigma^2 I)$ and a hierarchical model for the regression coefficient $\beta$ of a form ...
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1k views

Hierarchical (multilevel, random-effects) Gaussian process regression

If we have a $J$ groups of predictor, outcome (univariate) variable pairs, $$ \{(y_{j1}, x_{j1}) \ldots (y_{jn_j}, x_{jn_j})\}, \quad\text{for $j \in 1\cdots J$}, $$ a hiearchical linear regression ...
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1k views

Is this correct hierarchical Bernoulli model?

I have a question about correctness of a model that I used for a fairly simple experiment. I'm not sure if it should go to stackoverflow or crossvalidated, because I feel like my question is both ...
3
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0answers
1k views

Fitting a Bayesian Hierarchical Poisson Regression in R

I'm trying to fit a Bayesian hierarchical poisson regression. To do so, I'm using MCMChpoisson function from MCMCpack in R. Based on this package, the model is: $$Y_i \sim Poisson(\lambda_i)$$ $$\phi(...
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179 views

Bayes Net Parameter Learning in pymc

My goal is to infer the conditional probability tables (CPT) from the classic rain, sprinker, wet grass problem. Normally in this problem we know the CPTs and, given an observation like "the grass is ...
3
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68 views

Incorporating population priors into MLE fits with few/limited samples

I am fitting Beta distributions to data resulting from each of many experiments using maximum likelihood. My goal is for each experiment, given iid data $y_{1:k}$, fit a Beta distribution, and then ...
3
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186 views

Pymc: Does this model call for Index, and if so, how would I use it?

I'm working on speeding up the mcmc for a hierarchical pymc model that is taking .2 seconds per iteration. It's the second model from this paper, modeling a soccer league using team-specific attack ...
3
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0answers
172 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 ...
3
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427 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 ...
2
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24 views

Finding the mode of the posterior distribution

I have the following hierachical bayesian model - $\mathbf{x}|\mathbf{c},\sigma^2 \sim \mathcal{N}(\mathbf{x}|\mathbf{c},\sigma^2)$ $\mathbf{c}|\mathbf{c}_1,\sigma^2_2 \sim \mathcal{N}(\mathbf{c}|\...
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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: \begin{equation} 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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89 views

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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0answers
127 views

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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153 views

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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51 views

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 ...
2
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0answers
124 views

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 ...
2
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0answers
169 views

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 ...
2
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0answers
69 views

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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0answers
73 views

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 ...
2
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0answers
210 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' ...
2
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0answers
151 views

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 ...
2
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0answers
287 views

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 ...
2
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0answers
314 views

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 ...
2
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0answers
121 views

Seeking help in Bayesian Mixed Effects Model

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 = ...
2
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0answers
503 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 ...
2
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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{...
2
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0answers
515 views

Calculating the Deviance Information Criterion for a Hierarchical Regression Model

I'm not entirely sure how to phrase this question but maybe some background information might help. I am using MATLAB to perform hierarchical bayesian regressions and so I really need to understand ...
2
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0answers
133 views

Bayesian random effects

$\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) ...
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0answers
38 views

When are there analytic results for hierarchical-Bayesian models?

When, if ever, are there analytic solutions to hierarchical models? For example, under what conditions can we find an analytic form for the distribution of $X$ in the network below? $X$ has one ...