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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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### Bayes Factor for linear mixed models with BayesFactor package in R [on hold]

I am trying to compute the Bayes Factor (BF) for one of the fixed effect with the BayesFactor package in R. The data has the following structure: ...
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### How can parameters be modeled differently if they share hyperparameters?

In one popular example of multilevel Bayesian models (2007 Gelman et. al paper), radon exposure in a household is modeled as a function of the county and whether the house has a basement. In this ...
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### Multivariate Bayesian Car Model Result

I have developed a multivariate Bayesian Car model for three crash severity level analysis. I found that the covariance for both heterogenous effects and the spatial effect is not significant for any ...
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### Is appropriate to use empirical Bayes (EB) in this way?

Background. I have data from a study where participants make a series of judgments (a series of decisions with a binomial outcome, either $y=1$ or $y=0$). I have a model of the underlying decision-...
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### 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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### 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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### 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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### Bayesian updating of a probability density for evidence on its cumulative distribution

Suppose that I have a continuous variable E as a result of a simulation, which has a probability distribution as in the figure below: As seen from the cumulative plot, ...
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### ChoicemodelR - How to calculate variable importance using output of ChoiceModelR?

i have built a HB choice model using ChoiceModelR. Can someone tell me how to calculate the Relative Variable Importance from the output?
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### Bayesian Inference: Prior in Chinese Restaurant Process

For the Chinese restaurant process, as used in Dirichlet Process mixture models, we have a prior that data point i belongs to cluster j, where c is an indicator. n represents the total number of data ...
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### Statistical model suggestion for binary decision problem

I am looking for a statistical/machine learning model, which can describe and predict a (forced) binary decision between say A and B at any moment in time. I have input data from time series of say 3 ...
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### Proposal for correlation matrix with LKJ prior

I am writing a Gibbs sampler from scratch. As recommended in various places (http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n416.pdf, and in another question Covariance matrix proposal ...
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### Wrong sign of a model coefficient in Bayesian Poisson-Lognormal Car model

I am trying to develop a multivariate Poisson lognormal CAR model. One of my most important variables in the model is providing a negative sign which should be positive. However, when I develop a ...
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### Derivation of posterior for Bayesian hierarchical models

In Bayesian hierarchical models, the following posterior is used: $$p(\theta,\phi|y)\propto p(y|\theta)p(\theta|\phi)p(\phi)$$ I'm trying to derive this myself but when I use Bayes' rule, I get the ...
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### What are the necessary qualifications or assumptions to say that a graph structure is a Markov Chain?

I have a graph structure and want to say it is a Markov Chain. But I am wondering what necessary assumptions or properties that my graph structure need to meet to be called a Markov Chain?
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### How can I identify market regimes with a Hidden Markov Model?

I am trying to identify market regimes (2 states: bull or bear) with percent changes in equity returns. Can you help me in the mathematicl modeling of this? So far, I thought that for each day, there ...
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### Mixed Effects, Doctors & Operations: predicting on new data containing previously unobserved levels, and updating our confidence accordingly

Here's a quick sketch of a hypothetical situation. There are Doctors $\{1, \ldots, J\}$ who perform different types of operations $\{1, \ldots, K\}$. Our response variable is whether the operation ...
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### Use zeros trick for modeled parameters

Can the zeros trick be applied for specifying a new distribution for modeled parameters such as a varying intercept model? I am trying to estimate a hierarchial model (like the following) where I have ...
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### Probability distribution of the standard deviation of a gamma distribution

I want to generate some data using a series of Gamma distributions in a Bayesian hierarchical setting. I need to generate the data for a series of contexts, but I got only 2 data points per context, ...
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### 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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### Multilevel Negative Binomial fails with MLE

I have a pretty complex multilevel neg. binomial regression that does not converge when using a regular MLE (but from what I understand, when dealing with multilevel models, MLE is not regular, per se)...
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### Pseudo T-stat in Winbugs?

I am trying to obtain the "Pseudo T-stat" in Winbugs for a Poisson Log-normal model. Any suggestion of how can I get that.
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### 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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### Determine hyper-prior for gaussian distribution from existing data [closed]

Not sure how to determine hyper-prior for prior distributions, specifically using historical data. First what I am doing: I want to estimate parameters for a normal likelihood function using Bayesian ...
I am reading the paper by Griffin and Brown (2010) where at one step in their MCMC procedure they need to sample from the following conditional posterior:  p(\lambda|\gamma, \Psi)\propto \pi(\...