# Questions tagged [dirichlet-distribution]

The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.

229 questions
Filter by
Sorted by
Tagged with
0answers
15 views

### Treating missing data in making Bayesian inference

Suppose we have two biased coins $X_1,X_2$ that are possibly correlated to each other. In each round, when both the coins are tossed, there can be four possible outcomes: $(HH,HT,TH,TT).$ Let's ...
0answers
23 views

1answer
57 views

1answer
239 views

### How to use the Dirichlet prior for estimating the multinomial parameters? [closed]

I know that the multinomial distribution gives the likelihood of some vector D of occurrences to happen given a probability vector (parameters) P' i.e. P(D|P'). Now with a Dirichlet prior we are ...
0answers
72 views

### Understanding Multivariate Logistic Normal pdf

I'm trying to understand the Multivariate Logistic Normal distribution, in order to plot its pdf and compare it with a Dirichlet distribution. I believe I can follow the pdf derivation for the ...
1answer
102 views

### Bayesian posterior pmf for weighted dice with uniform prior

We want to find posterior probability mass function for dice tossing with uniform prior. We are interested in rolling of weighted dice. The outcome is 1,2,...,6. We assume that prior probability ...
0answers
58 views

0answers
25 views

### convergence issues moving from dirichlet to multinomial-dirichlet in JAGS (implemented in R)

I am modeling microbiome count data, using a multinomial dirichlet. The number of times I observe each microbial "species" depends on its fractional abundance within a microbial community, and the ...
1answer
30 views

### 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\\ &...
3answers
97 views

### Distribution of *conditional* frequencies when frequencies follow a Dirichlet distribution

Context: we have a large number of individuals characterized by two binary traits; call these $T$ with values $\{0,1\}$, and $T'$ with values $\{0',1'\}$. So there are four types of individuals: $00'$,...
0answers
43 views

### Recovering $\theta$ in Dirichlet-Multinomial (Polya) distribution

I'm working on Latent Dirichlet Allocation with Collapsed Gibbs Sampling. LDA has two Dirichlet-Multinomial distribution and one of them is a document-topic distribution that determines the ...
0answers
79 views

0answers
83 views

### Dirichlet process and clustering

How does clustering with a Dirichlet process as prior work? I am confused as to if the parameter $\alpha_i$ $\sim$ DP is found via clustering or is used to cluster. I undestrand how it can be used to ...
0answers
110 views

### Calculate Variance from Dirichlet-like Distribution Empirically

I'm interested in the proportion of time that a sensor is in a particular state. The sensor tells me the amount of time that it's in each state, which I will denote by $X = \{ X_1, X_2, X_3\}$. I ...