# Questions tagged [hierarchical-bayesian]

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

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### Extending the basic Bayesian medical diagnostic test

I have been thinking about the following problem that is often given in introductory bayesian text books. Suppose we have a medical procedure that tests for the presence of some disease. We want to ...
70 views

### Some hint for this exercise? (Bayesian)

I have the following problem (BDA3), but I'm confused, because actually, I have 2 samples, and I don't know how to set up just one model (of course is a multiparameter model, but how can I use the ...
413 views

### how to specify a distribution for left skewed data?

I am doing bayesian analysis. Exploratory analysis shows the parameter might has a left skewed shape. So what kind of distribution should I used as prior distribution for this parameter? Any kind of ...
364 views

### Tuning my proposal distribution - where does the tuning parameter go?

Suppose you are interested in sampling some parameter $x$. We sample proposals of $x$ (called $x^{*}$) from some normal distribution $q \sim N(\mu_{x},\sigma^{2}_{x})$. Denote $x'$ as all other ...
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 ...
134 views

### Bayesian updating in JAGS - data not reaching posterior distribution

I am trying to model the survival of a bird species as the function of a habitat variable, using JAGS run with the R package R2jags. When I leave the habitat variable out, I get believable estimates ...
583 views

### Difference between a fixed and random effects model equation-wise

I recently read a book that illustrated the difference between a fixed effects and a random effects model. It claimed the following: Let $k = 1, \ldots, K$ and $\hat{\theta}_k$ be our treatment ...
469 views

### In a Bayesian Hierarchical Model set-up, what is the definition and difference between random and fixed effects?

I understand that fixed vs. random effects have different meaning whether it be in biostatistics or econometrics. I recently came across a talk regarding fixed vs. random effects in the hierarchical ...
523 views

### Choosing error-variance priors in hierarchical models

I am trying to find a reasonable and largely uninformative set of priors for the error variance in a multi-level model. The model was developed by others, and I am unsure whether their choices were ...
149 views

### In calculating the Schwarz Criterion (BIC) what does the “number of samples” (n) mean?

The Bayesian Information Criterion is calculated with: $BIC = k\ln(n) - 2\ln(\hat{L})$ where $n$ is defined as the number of data points in $x$, the number of observations, or equivalently, ...
2k views

### How to calculate the Bayesian or Schwarz Information Criterion (BIC) for a multilevel bayesian model

The BIC is defined as (according to wikipedia) $BIC = k\ln(n) - 2\ln(\hat{L})$ where the likelihood $\hat{L} = p(x|\hat{\theta},M)$ where $M$ is the model, $x$ are the data, and $\hat{\theta}$ are ...
157 views

### throwing away all Gibbs samples after approximation

This is more of a theory question, consider: $$P(w_1|D)=\int P(w_1|S)P(S|D)d(S)$$ which we approximate via Gibbs sampling $S$ (assume the initial state of the Gibbs sampler is denoted by $M_0$), ...
363 views

### Hierarchical bayes

I am programming in R using hierarchical bayes for a choice-based conjoint task and wondering how I code the "none of the above" option in the design matrix? The <...
56 views

### What kind of book provides an introduction to free-energy minimization?

I have a basic understanding of free-energy minimization methods from doing some reading in neuroscience on prediction error minimization--primarily from Rafal Bogacz's beautiful tutorial on the free-...
1k views

### How does Hierarchical LDA compare to Hierachical Agglomerative Clustering?

I have a collection of documents and want to detect a hierarchy of named topics from them, what are the pros/cons for using hierarchical latent Dirichlet allocation (h-LDA) over hierarchical ...
62 views

### Sampling a pymc hierarchical posterior with small population sample size - Spread variance adjustment correction question

I've created a pymc poisson hierarchical model to forecast sports scores. If I use a smaller sample size of the season, say the first month, (10 games per team) versus using the entire season (100 ...
73 views

### How to set the index valued M in Hierarchical model to compute Bayesian model probability?

I'm incorporating a Bayesian Model Averageing(BMA) approach in my research and strapped in trapped in the estimated of Pr(theta|D). Professor John K. Kruschke(2014)'s book in chapter 10 offers an ...
616 views

### Bayesian 1 sample t-test (paired / repeated measures)

I'm a neuroscientist trying to move away from frequentist to bayesian statistics, please bear with me... I'm after a hypothesis test on some of my data: e.g., let's say I have reaction times for two ...
232 views

### 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 ...
954 views

### How can I re-code this hierarchical model in PyMC 3?

I wish to model data from an experiment using a hierarchical Bayesian logistic regression. The experiment involved many subjects, and many trials collected from each subject. The DV is the outcome of ...
69 views

### Shrinkage in hierarhical models based not on observations

When we have a hierarchical model, such as: $$log(y_{i,t})=\beta_0 + \beta_i*log(x_{i,t})+\epsilon_{i,t}$$ Where $\beta_i$ ~ $N(B,\Sigma)$, and the sampling model is normal (normal disturbances.) ...
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### Hierarchical Bayesian model or ensemble of predictors?

My model has 3 independent parameters $\{\rho, \alpha, \beta\}$ (polar coordinates), and a set of observables $\{Q_i\}$ and $\{T_{ij}\}$ where $i=1,2,...,642$ and $j=1,2,...,Q_i$ (if $Q_i=0$, there is ...
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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 ...
334 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 ...
2k views

### Use of Bayesian hierarchical model

What is the purpose of Bayesian hierarchical model? When should I use such models? I've found many questions here and references on the web but they are all too technical. My doubts are about the ...
223 views

### Translating user-defined joint-distribution from PyMC to PyMC3

I'm attempting to set up a simple beta binomial hierarchical model with an uninformative prior in PyMC3. I've read that the uninformative prior for this model should have alpha and beta hyper-...
429 views

### KL divergence for a hierarchical prior structure e.g. Linear Regression

For a Linear Regression $\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \epsilon$ with $\epsilon \sim \mathcal{N}(0, \sigma^2\mathbb{I})$, suppose the prior set on $\beta_k$ is $\sim \mathcal{N}(0, l_k)$ ...
298 views

### How to run a count time-series multi-level Bayesian regression in R?

I have an upcoming project that involves the following: A client will provide measurements of traffic counts on a daily basis over the period of a calendar year for about 60 out of 300 locations. ...
174 views

### pyMC produces values outside range of uniform distribution while sampling from Bayesian hierarchical model [closed]

I have a hierarchical Bayesian model consisting of a Uniform prior distribution, between a minimum and maximum value (hyperparameters) at the top level of the hierarchy. I sample a "mean" from the ...
238 views

### Probability distribution to represent group mean of multiple beta distributions

Say I have two coins from a particular mint in the US. I flip coin one 20 times and receive 4 heads, giving me a beta distribution for the bias of coin one of $Beta$($\alpha$=5, $\beta$=17). I then ...
148 views

### what is the use/meaning of taking the partial derivatives of a joint distribution?

This is probably too broad, but is worth asking: Assuming an unknown distribution (from which you would like to sample), is there any benefit in looking at the gradients of the joint with respect to ...
72 views

### How to construct prior for two variables based on known distribution of their product?

Building a hierarchical Bayes model, and I am interested in Bayesian inference of two parameters $a > 0$ and $b > 0$. Right now I am using uninformative priors on both $a$ and $b$. But I ...
31 views

### How do I model of Y| X, M when data has only X and Y not M, an upper bound on Y?

Suppose I have a set of Bernoulli random variables $y_j$, corresponding to molecules in an excited or unexcited state. I have a random variable $Y$ which is the concentration of the molecules in a ...