# Questions tagged [dirichlet-process]

A family of stochastic processes whose realizations are probability distributions

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### Parallel Tempering and Bayesian Non-Parametrics

In parallel tempering, we run multiple MCMC chains in an ascending temperature ladder, where the posterior density of the $i$th chain is exponentiated to the reciprocal of the temperature of the $i$th ...
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### Bayesian Hierarchical Clustering prior update

I am working through Heller and Ghahramani's "Bayesian Hierarchical Clustering" paper (https://www2.stat.duke.edu/~kheller/bhc.pdf) and things aren't quite working out the way I expect with ...
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### Inference on latent variable with observation of its convolution with itself

Problem I have an inference problem where the data observed are univariate random numbers whose distribution is obtained as follows. A latent random variable X is first sampled from a parametric ...
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### 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
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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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### Expected value (and variance) of a Dirichlet Process

Suppose I have a measure $G$ that follows a Dirichlet Process, $$G \sim DP(H_0,\alpha)$$ where $H_0$ is some base measure. Is there a closed form solution for the expected value of $G$?
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### Estimating the likelihood of a Dirichlet process

I am not sure if what I'm trying to achieve makes sense or is even possible, but I'd like to do MLE on a Dirichlet process mixture model. My reasoning is the following: If we can write out the ...
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### Can we use Dirichlet process to simultaneously estimate the number of mixtures and component distribution of a Bernoulli mixture?

Suppose I have a random sample on a Bernoulli random variable $\{X_i\}_{i=1}^N$ generated from model $p=\sum_{k=1}^K\pi_kp_k$,where $p\equiv Pr(X=1)$ and $p_k\equiv Pr(X=1|k)$, and $\pi_k$ are the ...
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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 $$\mathbf{X}\equiv(X_1,X_2)\sim\text{Dir}(\alpha_1,\alpha_2)$$ ...
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### Scoring rules for Dirichlet process mixtures

Let's say I do a sample-based fitting of a Dirichlet process model: \begin{aligned} X_i &\sim f(x_i\mid \theta_i)\\ \theta_i &\sim G\\ G &\sim \text{DP}(\alpha, G_0) \end{aligned} ...
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### Why does Chinese Restaurant Table Distribution look like a Gaussian Distribution?

The Chinese Restaurant Table Distribution describes the probability distribution for the number of non-empty tables in the Chinese Restaurant Process after $T$ customers have been seated. Specifically,...
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### Validity of BIC for Dirichlet process mixture models

I am implementing clustering using Dirichlet process mixture models via scikit learn's Variational Bayesian Gaussian Mixture model. I arrived at the appropriate priors iteratively, and I am able to ...
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### Clarifying Dirichlet Process Mixture Probability Terms

Suppose I have a Dirichlet Process Mixture model defined as follows: $\alpha \sim G(a,b)\\ \pi|\alpha \sim \text{Dir}(\alpha)\\ z|\pi \sim \text{Cat}(\pi)\\$ where $G$ is just a standard Gamma ...
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### Coding a simple Stick-Breaking Process in Python

I've just red the great 2012 blog post of Edwin Chen about Dirichlet Process with companion code in R and Ruby. Then I'm trying to translate the Stick-Breaking Process from R to Python. I've got this ...
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### Gibbs sampler for Dirichlet Process concentration parameter

I am trying to implement a Gibbs sampler for Hierarchical Dirichlet process, but I cannot seem to correctly estimate the concentration parameters. I therefore started testing just this part of a ...
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### HDP: Gibbs sampler implementation

I am trying to recreate the model proposed by Gao et al. (2011), based on the Hierarchical Dirichlet Process proposed by Teh and al. (2005). To estimate the model (let's call it iHDP) I need to ...
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1 vote
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### Dirichlet-Multinomial Distribution with many zero counts

Short version: Is there someway to make the dirchlet-multinomial distribution sensitive to the presence of zero counts? Long version: I am attempting model metric positions in musical data. You can ...
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### How to interpret graphical model for Dirichlet process mixture for variational inference?

I am working through this paper by Blei and Jordan, which introduces variational inference for Dirichlet process mixtures. They derive an evidence lower bound (ELBO) function based on a stick breaking ...
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