Questions tagged [multinomial-dirichlet-distribution]
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Construction of Dirichlet multinomial from independent negative binomials
I have a dataset with ISO3 country code, Year (from 2010 to 2019), Causes of death category (24 categories in total) and number of deaths. The sum of deaths across causes is fixed. My goal is to ...
2
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Dirichlet/multinomial dirichlet model with autocorrelation
I need to estimate an inferential statistical model of a variable that is a set of 8 proportions that sum to 1. The data repeat for 25 years and the series is an AR1 process. Is there a statistical ...
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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 ...
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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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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 ...
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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, $j$ ...
- 225
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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 ...
- 1,047
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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 ...
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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_{...
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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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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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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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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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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 ...
- 272
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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+...
- 272