Questions tagged [dirichlet-distribution]
The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.
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Mapping two Dirichlet Distributions into a comparative Dirichlet
Assume I observe some draws from 2 choice options, and want to infer the probabilities of various outcomes, e.g. non-negative integers up to a limit L. I could simply use 2 Dirichlet distributions to ...
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Difference between hierarchical dirichlet process and nested dirichlet process
There have some extensions to Dirichlet process. One is Hierarchical Dirichlet process, and another is Nested Dirichlet Process. What are the differences between these two?
I once read the paper of ...
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Definition of distribution conditioned on both a categorical and Dirichlet prior
If we have a conditional categorical distribution, with unknown parameters, we can represent with a table, as in the example below:
\begin{align*}
&z \quad P(z|\theta)\\
&0 \quad \theta_0\\
&...
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Combining Dirichlet and Gamma-Normal distributions
I have a model that describes 2 dimensional data where each data points is define as d = [category, x].
The category dimension can take 3 different values with respective probability $p_1$, $p_2$ and $...
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What is a representation of positive numbers summing to one that can be sampled via HMC?
I have a probability density $f(x): \mathbb{R}^n \rightarrow \mathbb{R}$ whose argument vector $x$ satisfies the constraints that all elements are positive and sum to unity. I need to generate samples ...
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Zero-Inflated Dirichlet
I want to set up a model that will rely on something similar to a zero-inflated Dirichlet distribution. As such, I'm trying to figure out how a zero-inflated Dirichlet distribution is set up from the ...
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How to calculate the expectation of the following Dirichlet distribution and Beta distribution?
This is a question from my research, related to the derivation of the variational EM algorithm with mean-field assumption about LDA-based model.
We all know, given that $\boldsymbol{\theta} \sim \...
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How to derive the expectation of $\log[a \theta_k + b]$ in Dirichlet distribution?
Given that $\boldsymbol{\theta} \sim \mathrm{Dir}(\boldsymbol{\alpha})$, then $E_{p(\boldsymbol{\theta} \mid \boldsymbol{\alpha})}[\log{\theta_k}] = \Psi(\alpha_k) - \Psi(\sum_{k'=1}^K \alpha_{k'})$, ...
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Multivariate proportional data
I am looking for literature on what I call multivariate proportional data where a single observation is a vector of proportions that sum to 1. For example, each person weights their preferences for ...
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Distributions on the simplex with correlated components
I'm looking for some kind of distribution over the simplex in which components are correlated in an ordinal way. That is, if $p = (p_1, ..., p_J)$ is drawn from our distribution on the simplex, I ...
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Reparameterization trick for the Dirichlet distribution
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My aim is to create a (probabilistic) neural network for classification that learns the distribution of its class probabilities. The Dirichlet distribution seems to be choice. I am familiar ...
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Reference request: generalized linear (mixed) model for Dirichlet distribution
Plenty of books about on GLMs for exponential families, but any good books or papers which study the Dirichlet distribution in particular?
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Bayesian inference based on a 3$\times$3 contingency table
How do I make inferences about population parameters based on a 3$\times$3 table of observations? In "Bernoulli's Fallacy", Aubrey Clayton provides this (Table 5.8).
Democrat
Republican
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Dirichlet sample by normalising Gamma RVs
I know that if you sample $K$ random variables $(X_1, X_2, \dots, X_K)$ from Gamma distributions using shape parameters $(\alpha_1, \alpha_2, \dots \alpha_K)$ and a scale parameter $\theta = 1$ such ...
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Find marginal distribution of $K$-variate Dirichlet
I've already seen https://math.stackexchange.com/questions/1064995/marginal-of-dirichlet-distribution-is-beta-integral, but need to extend this to the $K$-variate case.
We have $\mathbf{x} = \begin{...
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