# Questions tagged [hierarchical-bayesian]

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

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### Normalizing constant irrelevant in Bayes theorem?

I've been reviewing Bayesian literature in an attempt to utilize Bayesian inference for hypothesis testing when I have very well established priors, but there's one thing I cannot get my head around: ...
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### What are some statistical tests for exchangeability of a data set?

The representation theorem of de Finetti is seen by some as motivation for the use of Bayesian and/or hierarchical modeling. In some settings, it may be plausible to assume measurements are ...
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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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### Relation between Bayesian analysis and Bayesian hierarchical analysis?

I have been studying a Bayesian hierarchical model. In that model all I am dealing is with the estimation of parameters. In Bayesian analysis, loosely speaking, we update our prior knowledge (in light ...
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### Multi-level Bayesian hierarchical regression using rjags

I am trying to to implement a Bayesian hierarchical Model in R. I have a few predictor variables (2 metric and one categorical) and am trying to predict quarterly home sales in the US. Each sales ...
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### Flipping random coins from a bag - equivalent to a single coin?

My first and I think naive question here. I am trying to model a certain business, and the simplest model I am willing to test is: 1. there is a bag of differently biased coins. 2. every step, a ...
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### How to choose t-distribution degrees of freedom in “robust” Bayesian linear models

It is well known that in both frequentist and Bayesian linear models, outliers can greatly influence the parameter estimates. Consider the simple example where one outcome variable, $y$, is predicted ...
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### Setting up a MCMC scheme for Multivariate Stochastic Volatility

I want to understand the survey of Lopes and Polson (2010) regarding MV stochastic volatility. Assume the $p$-dimensional vector $y_t$ follows $$y_t\sim N(\Theta,\Sigma_t).$$ In order to model the ...
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### Gibbs sampling with mixed prior using a Metropolis-Hastings step

My questions are about a sampling procedure for ﬁtting a Bayesian hierarchical model where one of the priors is a mixture distribution of discrete and continuous parts. The model is not my own but I ...
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### Metropolis-Hastings acceptance rate confusion

I ran a Bayesian model that have about 2700 parameters. Among these parameters, Adaptive Metropolis algorithm was implemented to estimate ~790 parameters in the I-group and Metropolis algorithm was ...
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### Stick-breaking construction of Dirichlet process

In the stick-breaking construction of Dirichlet (let me base things on Sethuraman's construction - slide 6 of this) do we sample one $\phi$ vector from the base distribution $H$ and use it for ...
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### 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 ...
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### 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 $\sim \mathcal{N}(0, l_k)$ ...
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### Interesting / strange behavior of one chane on different [unrelated] variables in STAN

I have a quite complex hierarchical model for which I'm estimating parameters and producing posterior predictive using STAN (rstan) for some psychophyiscal data. I'm (sometimes) observing some ...
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### Need help deriving a gibbs sampler for a normal mixture model with two components

Let $\theta_i$ be an indicator that the i-th eruption is a long eruption. (i.e. $\theta_i = 1$ if the i-th eruption is long and $\theta_i = 0$ otherwise.) Assume the following model and derive a Gibbs ...
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### Data Conversion to Standard data format in hierarchical Dirichlet process

I'm trying to test the performance of posterior inference on a set of documents with hierarchical Dirichlet process for topic modeling. How can i convert my data (document) to standard data format ...
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### 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 ...