# 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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### Choosing a probability distribution for 4D data: dirichlet challenges and alternatives

I'm seeking the right distribution for my 4D data, where the sum of values in each sample equals one. Currently, I've chosen to employ the Dirichlet distribution. However, upon applying this ...
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### Stick-breaking construction of Dirichlet distribution vs Dirichlet process

Let $F_0$ be some probability measure and $\alpha > 0$ be the concentration parameter. I can draw a random distribution from $F\sim \mathrm{DP}(\alpha, F_0)$ using the stick-breaking construction: \...
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### Dirichlet Regression output and using the calculated coefficients in regression model

I am very new to Dirichlet Regression and trying to make sense of the output and the regression coefficients. I am doing a biomass study and have tested the following variables (DBHH, DBH + H, DBH and ...
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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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### Bayesian updates for Dirichlet-multinomial with Gamma prior

Let \begin{aligned} X_i &\sim \text{Dir-multinom}(X\mid\lambda)\\ \lambda_{j} &\sim \text{Gamma}(\lambda_j\mid\alpha,\beta)\\ \end{aligned} where $i$ iterates over observations, $j$ ...
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### Computing a prior from two components in Naive Bayes

Given a model parameter $\theta$ that is composed of two distributions in a Naive Bayes classifier, how is $P(\theta)$ typically computed in practice? More specifically, from the article of Nigam et ... 84 views

### Mixtures of Dirichlet multivariates or Dirichlet processes

I am exploring the properties of Dirichlet distributions and their parameters. When mixing two Dirichlet distributed random bivariates $$\mathbf{X}\equiv(X_1,X_2)\sim\text{Dir}(\alpha_1,\alpha_2)$$ ...
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### Dirichlet distribution parameters from known variances

Let's assume, I know the variances of Dirichlet distribution parameters. Let these variances be: $Var[X_1], ..., Var[X_n]$. Is there a analytical solution to derive the parameter value alpha_i given ...
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### Sum of squares for a Dirichlet distribution

I have some data that takes the form of vectors $(a_0,...,a_n)$ lying on the simplex $\Sigma a_i = 1$ (all $a_i$'s non-negative). I have noticed that the maximum $\max_i a_i$ is very highly correlated ...
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### Reparameterization trick for the Dirichlet distribution

Summary: 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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### Using the methods of moments in R for the dirichlet distribution

I'm trying to build a distribution of transition probabilities to randomly sample from in a Markov model where individuals can transition from one health state to another (assume that in the image ...
We know that a random variable $p=(p_{1}, p_{2},..., p_{K})$ which follows a $\textit{Dirichlet}$ distribution with parameters $\textbf{a} = (a_{1}, a_{2},..., a_{K})$ has as pdf $$f(p) = \frac{1}{B(\... 0 votes 0 answers 165 views ### How is a convex combination of Dirichlet-distributed variables distributed? Let X = (X_1, \dots, X_K) \sim \operatorname{Dir}(\alpha_1, \dots, \alpha_K) and define the convex combination Y = \sum_{i=1}^{K} c_i X_i. In the case of K=2, the constraint \sum_{i=1}^{K} X_i =... 3 votes 1 answer 142 views ### Bayesian (continuous) logistic regression model with Beta likelihood? I have a problem where my target variable are continuous/float values in the range [0,1]. If my data were integers in {0,1} this would be a simple logistic regression / Bernoulli likelihood problem. ... 0 votes 0 answers 163 views ### Dirichlet-distribution and its correlation? I have the following variables that follow a beta distribution: ... 5 votes 1 answer 258 views ### Mean of Generalization of the Dirichlet Distribution I know that if X_{1},X_{2},...X_{n} are independent \mathrm{Gamma}(\alpha_{i},\theta) - distributed variables (notice they all have the same scale parameter \theta) and Y_{i}=\frac{X_{i}}{\sum_{... 1 vote 0 answers 306 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.... 3 votes 1 answer 708 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 1 answer 85 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 ... 4 votes 1 answer 972 views ### How to visualize Dirichlet distribution (with more than 3 targets)? 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 ... 1 vote 1 answer 298 views ### Stationary distribution of a Markov chain with a random transition matrix 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)$$and we ... 1 vote 0 answers 150 views ### Log-likelihood of a finite mixture distribution (PDF overflowing) I'm trying to use a finite mixture of Dirichlet distributions in a project, but am encountering problems with the PDF becoming so large for input values close to 0 that it overflows to infinity (as ... 2 votes 1 answer 115 views ### Upgrading weight parameters to random variable in Gaussian mixtures In a Gaussian mixture model we model a density like: p(\mathbf{x}|\pi,\mu,\sigma)=\sum \pi_i N(\mathbf{x}|\mu_i,\sigma_i)  where \pi,\mu and \sigma are parameters. I would like to know if the ... 3 votes 1 answer 300 views ### Difficulties in computing the derivatives of the Dirichlet distribution I need to compute the first derivatives of the Dirichlet distribution, defined in the following way:$$r(P; \pi, \rho) = \frac{\Gamma(c)}{\prod_{i=1}^{k} \Gamma(c \pi_i)} \cdot \prod_{i=1}^{k} P_i^{c\...
Suppose that each in a set of $n$ random variables $\boldsymbol{X}_1, .., \boldsymbol{X}_n$ are Dirichlet-distributed with parameters $\boldsymbol{\alpha}_i$, where $i$ is an index for the random ...