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# Questions tagged [multinomial-dirichlet-distribution]

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### Posterior predictive distribution for Bernoulli (and categorical)

I'm trying to confirm something I've tried to figure out about the posterior predictive distribution for Bernoulli vs. Binomial (and categorical vs. multinomial) random variables after a Bayesian ...
66 views

### How to fit Multinomial-Dirichlet regression for correlated compositional count data in R?

I have compositional data where $K$ compositions (the abundance of $K$ cell populations) are measured on $n$ samples at baseline and repeated at 1 or more follow-up times. The $n$ samples are divided ...
241 views

### 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, $j$ ...
40 views

### Expected value of log(gamma function(Dirichlet variable))

The following problem emerges from coordinate ascent variational inference in a mixture model with Dirichlet-Multinomial components. I want to compute the expectation of the log likelihood. Since my ...
1 vote
202 views

### Expectation maximization: does the likelihood always increase monotonically?

When working with (gaussian) mixture models, I always took it for a mathematical fact that the marginal likelihood increases with every iteration step. If it were not the case, it always meant an ...