# 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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### 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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### Why do proportions hold across credibility range in multinomial distribution? How to compute probability of deviations from that?

I know I can use pymc3 code like this to find out if die is biased and what side is it that is more prone to show up (taken from here). ...
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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 ...
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### Variational Autoencoder with Dirichlet distributed latent space using the Weibull Distribution

My goal is to create an VAE with an Dirichlet distributed latent space. Since the reparametrization trick does not work for the Dirichlet Distribution, I am trying to approximate the Gamma ...
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### 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 $$\mathbf{X}\equiv(X_1,X_2)\sim\text{Dir}(\alpha_1,\alpha_2)$$ ...
1 vote
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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 ...
66 views

### 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 ...
121 views

### 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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### Dirichlet distribution concentration parameter [duplicate]

Suppose I have a categorical distribution with 4 possible states and I want a Dirichlet distribution over it and I want every discrete state to be equally probable. I am slightly confused about the ...
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### Single-value alpha parameter for Dirichlet distribution

I'm trying to implement an event schema induction method from a paper from 2015. The authors use a generative approach to learn a language model. For this, they use a lot of probability distributions ...
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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 ...
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### Question about the distribution of the average of Dirichlet-distributed random variables

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 ...
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### Deriving the marginal multivariate Dirichlet distribution

I am trying to understand how my professor (see derivation below) has derived the multivariate marginal distribution of a subvector of $\theta_j$´s from a Dirichlet distribution. I understand ...
1 vote
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### Restriction and dependence in the Dirichlet distributon

The Dirichlet distribution is sometimes said that it is "too restrictive and imposes strong conditions on the dependence between components". What is the reason?
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### Overall variance of a Dirichlet distribution

I have observations on proportion of individuals at different age groups. I'm doing some simulation experiments, and I need to introduce error in the observed data. For that, I'm simulating data from ...
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### Marginal Cluster assignments for Dirichlet Process mixture model

I am watching Tamara' Broderick video on Dirichlet Process mixture models where she talks about computing $p(z_n = k | z_1,z_2,..z_{n-1})$ at ardoun 16:06. The z's are drawn from \rho_1 \sim beta(...
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### How to derive the expectation of $\ln \mu_j$ in Dirichlet distribution

I have derived the mean and variance of $\mu_j$ in Dirichlet distribution $\text{Dir}(\mu_1, \cdots, \mu_K|\alpha_1, \cdots, \alpha_k)$. On https://en.wikipedia.org/wiki/Dirichlet_distribution, it ...
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### What is a non-informative choice of parameters for a Dirichlet distribution?

Dirichlet distribution is a conjugate prior for multinomial distribution. I want to impose a non-informative prior over sampling weights $\pi$ for a draw $x=(x_1,…,x_N)$ from a multinomial ...
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### Uniform posterior on bounded space [duplicate]

In a particular Bayesian problem, I have encountered a choice of parameters that leads to a uniform posterior distribution. Given prior p(\boldsymbol{\pi}) =Dirichlet(\boldsymbol{\...
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1 vote
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### How to model proportions with a hierarchical structure?

I have thinking about how to model proportions for a problem with hierarchical structure. In the problem, I have observations of users over multiple days, where each observation is a proportion of ...
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1 vote
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### Softmax vs the Dirichlet distribution

As far as I understand one can in principle model the distribution over a set of $k$ categories using e.g.: the Dirichlet distribution A softmax model. As far as I can tell, both use $k$ parameters ...
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### How does the uniform Dirichlet PDF integrate to 1?

For the uninformative 3-dimensional Dirichlet prior ${\rm Dir}(1, 1, 1)$, I understand that the probability density function (PDF) evaluates uniformly to 2, and the support are all three-dimensional ...
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### On posterior in the Bayesian bootstrap

The Bayesian bootstrap was introduced by Rubin (1981) as a Bayesian analog of the original bootstrap. Given dataset $X=\{x_1, \dots, x_N\}$, instead of drawing weights $\pi_{n}$ from the discrete set \$...
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### Fitting/Inference for Dirichlet Process/CRP for clustering

Please excuse my ignorance on this topic, I don't have much experience in nonparametric Bayes. I read about Dirichlet process clustering and the Chinese Restaurant Process analogies. I think I ...
2k views

### Dirichlet distribution vs Multinomial distribution?

Both Dirichlet and multinomial distributions are distributions over vectors, and both Dirichlet and multinomial distributions are constrained so that all of the elements of these vectors sum to a ...
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