Questions tagged [hierarchical-bayesian]

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

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Hierarchal Bayes: logistic regression

We have the following model that was proposed to me. It takes yes, no and maybe responses to try and predict attendance $y_{i}$. $$ \begin{align} y_i &\sim \mathsf{Bin}(n, p_i) \\ p_i &= \...
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264 views

Using PyMC3, how could I force a maximum to posterior distribution?

I am pretty new to bayesian statistics and PyMC3. I am doing a hierarchical model where the output variable I am trying to predict is a percentage with a maximum of 100%. My problem is that my ...
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237 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 ...
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Hierarchial Bayesian approaches versus simple prior based approaches

The point of Hierarchical Bayesian models is that you can get parameters for different "hierarchies" within your data. For example, if you have 10 data points for one person, 10 for the next and so on,...
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Understanding covariance in Bayesian regression model

I am confused about when to model covariance in a Bayesian regression. Here's what I am trying to model. I have a dataset which has scores for a set of students who did a set of practice exam problems....
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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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388 views

Problem with “log(0)” error while using brms in R to do Bayesian analysis [closed]

I'm using brms to conduct a multilevel regression in R. I've been getting warnings and errors of the following type: ...
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1answer
100 views

Selecting Bayesian priors for the dependent data

I have goal of measuring CTRs of several titles of an article on a website using Bayesian approach. In a simple setup, what one will do is to select Beta Prior (for example Uniform distribution) and ...
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184 views

Hierarchical linear modelling in R

I am trying to build a hierarchical linear model based on data structured like this dataset below. The model form I am looking to build is Purchased ~ f(price + color + more item attributes + age + ...
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52 views

Robbins estimate Empirical Bayes

From the compound sampling model where: $Y_i | \theta_i \sim Poi(\theta_i)$ The marginal distribution of $\theta_i$ is $G$, non-parametric. We get that the Bayes estimate of $\theta_i$ under ...
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53 views

Best modeling approach for “two-factor varying slope” model?

I'm new to this forum so I hope this question is appropriate. Please let me know if there is anything I can do to improve the question. I simply have a situation in which I am considering the best ...
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131 views

Are predictive distributions supposed to be distributions of future data?

In frequentist analysis, we define a 95% prediction interval as an interval that will contain the next observation 95% of the time under repeated sampling of the entire experiment and prediction. If ...
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411 views

How to self-define likelihood with dmulti() in JAGS?

I am running a hierarchical Bayesian model and would like to use the "ones trick" to self-define a likelihood function, just to prevent the problems that dmulti() may have with zeros. To be able to ...
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79 views

re.form specifying one random effect but not the other

I have fitted a multilevel model using stan_lmer that has two sets of varying intercepts, one for categories and one for subjects. The code essentially looks like ...
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84 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 ...
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Why LKJcorr is a good prior for correlation matrix?

I´m reading the chapter 13 "Adventures in Covariance" in the (superb) book Statistical Rethinking by Richard McElreath where he presents the following hierarchical model: (...
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94 views

Merging Bayesian and frequentist models

I have two models. One is a hierarchical Bayesian model that estimates parameters $p_{i, j}$ for group $i$ and sex $j$. This model is set up hierarchically because of the inherent structure of the ...
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242 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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115 views

Standard Deviations of Random Effects

I would have a question regarding the estimates of the random effects for a model fitted with JAGS. I want to fit a mixed model of the form: $$y_{ij}=\beta_{0j}+\beta_{1j}x_{ij}+\beta_2+e_{ij}$$ $$\...
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409 views

Attempting to compare Bayesian and Frequentist mixed effects models

This question may be better suited for stack overflow (happy to move it if deemed too off topic). I am currently in the process of learning Bayesian analysis using stan in R as my software. ...
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305 views

Why does the redundant mean parameterization speed up Gibbs MCMC?

In Gelman & Hill (2007)'s book (Data Analysis Using Regression and Multilevel/Hierarchical Models), the authors claim that including redundant mean parameters can help speed up MCMC. The given ...
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278 views

Bayesian inference on mean of statistic from population

Suppose that a collection of time intervals $t_i$ have occurred, for $i=1,...,n$. These should be considered as samples from a population governed by some distribution. During these time intervals, ...
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157 views

Specification of priors for multivariet hierarchical regression using MCMCglmm

I'm analyzing data from experiment, where people had to select a point in plane. I'm trying to asses which atributes of the task and personality are asociated with the outcome. Becouse we used ...
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28 views

What distributions might describe the percentage of a population with a trait across groups?

Suppose I have a large number of urns, each with a different ratio $r$ of white and black balls. Some urns may be full of white balls or full of black balls. What kinds of distributions or processes ...
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232 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 ...
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294 views

Ergodicity of MCMC in a hierarchical model

Many of the Bayesian hierarchical models that I am studying use a Markov chain as the model. These hierarchical models use different MCMC techniques to sample low-level and high-level parameters. My ...
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1k views

Seeking a closed form for a posterior distribution

In the book Bayesian Data Analysis by Gelman et al. (3rd edition, 2014), a hierarchical model (or one-way random-effects ANOVA) is presented in section 5.4 as follows, \begin{equation}\label{eq:...
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32 views

learning a gaussian distribution through dependent vairiable observations

Is it possible to infer the parameters of a gaussian random variable by sampling from a distribution that is linearly dependent on the variable of interest? For example: y = Ax + n With x ~ N(u,S) ...
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71 views

Gaussian Latent Variable Parameter Learning

Do any approximate (preferably message passing type) inference algorithms exist for learning the parameters of a latent Gaussian variable (from information of other dependent observed variables)? ...
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212 views

Bayesian output vs frequentist. Which should I rely on? MLM/ RE HLM

I have 2 questions. 1)My Bayesian output is providing some trouble. I have data that will vary across 5 countries. This means my group level has a small n of 5. This results in my data hovering ...
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31 views

What models predict higher levels of hierchical structure?

The wikipedia page for multilevel model states: The dependent variable must be examined at the lowest level of analysis. I am interested in predicting measures at higher levels of analysis. In ...
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840 views

In Bayesian statistics, what do mu, eta, and tau tend to represent?

In the eight schools example from Gelman, he sets his parameters as mu, eta, and tau. ...
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155 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 ...
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270 views

Comparing top level group effects using a 3-level hierarchical regression

I would like to detect group effects (if any) along with statistical confidences. I have a hierarchical data set structured as follows: Drug Groups ...
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247 views

Variational Bayes for Multivariate Normal distributed data with shared mean and precision

I have a model represented in graphical model and part of this model states that there are N data points that are generated from multivariate normal with shared mean vector and covariance/precision ...
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58 views

Meaning of Intercept Parameter in a Bayesian Longitudinal HLM

I have been working through John Kruschke's excellent book on Bayesian Data Analysis but now have found myself in experimental-design territory not covered in the book: a longitudinal linear mixed-...
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1answer
314 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 ...
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732 views

Simulate a sample of the posterior predictive distribution in a Bayesian hierarchical model

Suppose the following Bayesian hierarchical model: $$ Y|\lambda\sim\text{Pois}(\lambda) $$ $$ \log(\lambda)|(\mu,\sigma)\sim N(\mu,\sigma)$$ $$ \mu\sim N(0,10) $$ $$ \sigma\sim\text{Gamma}(0.01,0.01).$...
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326 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 ...
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33 views

How to model whether discrete count data are statistically-enriched in certain regions for spatial data?

I feel like there is a straightforward way to model this dataset, but I'm a bit stuck. Let me give you a metaphor for the data first: Let's say that we are looking at a strip of land of fixed ...
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352 views

Multilevel logistic regression in R: ML vs. Bayesian estimation

I hope you can help me with an issue I encountered while trying to build a multilevel logistic regression model in R. I get different results depending on whether I fit the model using Maximum ...
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114 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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114 views

Help! Newton-Raphson explodes!

I am trying to find the posterior mode of a log likelihood in order to implement maximum a posteriori. The parameter I am trying to estimate is actually a vector. I can find the first and second ...
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1answer
35 views

Multi-level models and residuals

As one increases the number of levels in a multi-level model, should one expect the output model variance to go down? That is, as we increase levels in our model: Full pooling: $y_i \sim \text{N}\...
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95 views

Left or right skewed prior in WinBUGS

I am trying to find a proper way of defining a right or left skewed continuous (0...100) distribution for my priors in a simple linear regression. Furthermore, I expect to find some outliers in my ...
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112 views

Gibbs Sampling / Monte Carlo with Weights

Consider pairs of data and their population weights $(y_i, \omega_i), i = 1, 2, \dots$ alongside some hierarchical structure, $$y_i\leftarrow\theta_{i(j)} \leftarrow \gamma$$ where $i(j)$ is perhaps ...
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31 views

Multilevel modelling of effects for positive values: Which distributions to use

I am currently trying to figure out what would be the best way to model a bayesian hierarchical regression for data, where the criterion value can only be positive and I am assume that the effects are ...
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48 views

How to put a prior on parameter “x” instead of parameter “y” if x and y are related

Background: I'm new to the Bayesian approach and thus am trying to better understand the multi-level (i.e., hierarchical) nature of the Bayesian approach. Question: Suppose I have a parameter ...
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547 views

Difference between Bayesian Hierarchical Model and a Bayesian regression model?

Are Bayesian Hierarchical models and Bayesian regression models the same in books, papers?
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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 ...