All Questions
9
questions
2
votes
0
answers
23
views
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 ...
- 21
4
votes
2
answers
645
views
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 ...
2
votes
2
answers
88
views
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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- 346
2
votes
2
answers
344
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, $j$ ...
- 225
7
votes
1
answer
275
views
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_{...
- 101
1
vote
0
answers
147
views
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 ...
- 150
3
votes
1
answer
256
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 ...
5
votes
1
answer
1k
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 ...
- 272
1
vote
1
answer
510
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+...
- 272