Questions tagged [multinomial-dirichlet-distribution]

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Bayesian network: graph synthesis & data sampling

Input (What I have): some Bayesian networks (both graph structure and conditional probability distribution (cpd)) and corresponding categorical datasets (e.g. bnlearn repo). Output (What I want): ...
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141 views

Using categorical data to build a Dirichlet distribution

I am building a graphical model. I have some categorical data $\boldsymbol{\mu}$ where they are generated by $p(\boldsymbol{\mu}|\boldsymbol{s},\mathbf{A})=\prod_k\prod_j\mathbf{A}_{ij}^{\mu_is_j}$. ...
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Why is Latent Dirichlet Allocation based on word sequences and not counts?

I assumed that LDA was a bag-of-words approach and that words could be exchanged within a document. However, reviewing more in-depth the Gibbs sampling equations, I noted that the compound Dirichlet-...
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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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1answer
39 views

How to find MLE for multinomial distribution and Expectation of X1 and X2

There are 3 types of flowers that can grow from planting a seed. $$P(\text{Daisy}) = \theta_1$$ $$P(\text{Rose}) = (1-\theta_1)\theta_2$$ $$P(\text{Sunflower}) = (1-\theta_1)(1-\theta_2)$$ The total ...
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316 views

Multinomial distribution: probability that one outcome is greater than another

Consider a multinomial distribution with three outcomes. Let $x_i$ denote the number of occurences of the $i^{th}$ outcome, and the $i^{th}$ outcome occurs with probability $p_i$, $i=1,2,3$. Let $n$ ...
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1answer
110 views

Multinomial-dirichlet with fractional counts

Suppose a lepidopterologist wants to estimate the relative proportions of three different species of butterfly. They go out into the field and count $N$ butterflies and record the number of each ...
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1answer
519 views

How is the mode in Dirichlet-Multinomial calculated?

The mode in Dirichlet-Multinomial is $$ \mathrm{Mode}(\pi_i) = \frac{\alpha_i + x_i - 1}{\sum_{j=1}^k (\alpha_j + x_j -1)} $$ Could you point out how is it calculated please? What is the importance ...
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183 views

What are the possible estimates of the parameters of the multinomial distribution?

The expected value of the parameters of the multinomial distribution (taking into account the Dirichlet prior $D(\alpha)$ and the posterior Dirichlet-Multinomial) is: $\pi_i = α_i+ x_i / \sum_{j} α_j+...
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115 views

Why there are not (long tail) alternatives to dirichlet-multinomial (while there are for posisson-gamma)

While there are a lot of long tail alternatives to poisson-gamma (negative binomial), for example (Source) I haven't found any work on replacing the dirichlet distribution with a more long tailed ...