# Questions tagged [dirichlet-distribution]

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

314 questions
Filter by
Sorted by
Tagged with
12 views

### 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 ...
22 views

### 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 ...
1 vote
71 views

### 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 ...
• 225
1 vote
68 views

• 93
645 views

### Dirichlet distribution with correlated components?

I am working with models that use Dirichlet distributions. However, I want to account for correlations between components. If this question is a duplicate, I'd also appreciate any pointers to the ...
1 vote
41 views

### A confusion about computing transformation of random variables

Let $(X,Y)$ be a pair of random variables with joint pdf $f_{XY}$. Let $(U,V)$ be two random variables obtained from $(X,Y)$ by $U = u(X,Y)$ and $V = v(X,Y)$ where $u$ and $v$ are, say, nice ...
• 11
19 views

### number of parameters in Dirichlet Mixture Model clustering (non-bayesian)

I made a function that implements the clustering algorithm in the research article "Clustering compositional data using Dirichlet mixture model" (2022). I am now trying to figure out which ...
1 vote
65 views

376 views

### Computation of ratio with Dirichlet distribution

I would like to compute ratio of proportions coming from a Dirichlet distribution. My understanding is that each proportion should be treated as a random variable and therefore I should use Taylor ...
• 51
1 vote
97 views

### Advice on how to solve a constrained KL Divergence problem between a Dirichlet and a Logistic Normal

I would like some advice or path to follow to solve the following problem. Consider a random variable $Y$ that follows a Dirichlet distribution $Y \sim Dir(\alpha)$. Let $X$ be a member of the ...
• 76
1 vote
21 views

### How can we measure the "fit" between the softmax outputs and Dirichlet distribution?

For simplicity, I'll consider classification with 3 classes. Then, softmax outputs can be considered as the set of points in 2-simplex. I want to measure the 'fit' of this softmax output with target ...
• 11
1 vote
197 views

### Ordinal regression - 'induced Dirichlet' conditional posterior distribution

I am trying to implement the 'induced Dirichlet' prior model proposed by Michael Betancourt (from section 2.2 of his ordinal regression case study here: https://betanalpha.github.io/assets/...
• 11
23 views

### Cross validation on bootstrap data

I am performing a dirichlet model for different species using a small sample size (between 8 to 20 samples per each). Since my dataset is small, I bootstrap my data with 1000 iterations, averaging 3 ...
103 views

• 11
1 vote
138 views

• 2,286
200 views

• 101
1 vote
456 views

### Approximating the Logit-Normal by Dirichlet

There is a known approximation of the Dirichlet Distribution by a Logit-Normal, as presented in wikipedia. However, I am interested in the reverse, can I approximate a logit-normal by a Dirichlet? I.e....
• 111
814 views

### How to generate data from a generalized Dirichlet distribution?

I need to generate data from a generalized Dirichlet distribution in Python to test my model, but I have no idea how can I proceed with that, can anyone guide me?
1 vote
96 views

### Concentration Bounds for categorial distribution with good Dirichlet prior

I would like to know if there are any standard methods for analyzing the concentration bounds (for example Hoeffding's bound) for a multinomial distribution modelled with a Dirichlet prior, with the ...
• 131
I want to plot a Dirichlet distribution $\operatorname{Dir}(\alpha), \alpha=[\alpha_1, \alpha_2, \ldots,\alpha_n]$. However, when I google it, almost all of the results consider 3 targets ($n=3$), and ...
Consider a Markov chain $\{X_t\}$ on a finite state $\mathcal{S} = \{1,\dots, S\}$ space whose transition matrix $P$ is populated by elements of the form $$p_{ij} = P(X_{t+1} = j | X_t = i)$$ and we ...