Questions tagged [dirichlet-distribution]
The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.
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Dirichlet Regression output and using the calculated coefficients in regression model
I am very new to Dirichlet Regression and trying to make sense of the output and the regression coefficients. I am doing a biomass study and have tested the following variables (DBHH, DBH + H, DBH and ...
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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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Bayesian reparametrization are they equivalent?
Suppose that we are in a Bayesian context, we we have the following matrix $n,$ $K\times K,$ as parameter, and we assume that
$$n_{ij}\sim Pois(w*w_{ij})$$
where $w\sim Gamma(N+1,1)$ and $w_{ij}$ is ...
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Classifying changes in Dirichlet distribution over time?
I'm interested in studying user preferences regarding streaming content. Given a discrete number of categories (ex: adventure, horror, comedy, family, drama) and the amount of time a given user ...
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Distribution of the ratio of Dirichlet/Gamma variates
It can be seen that the following random variates have the same distribution:
$\frac{X_1 + X_3}{X_2 + X_3}$, where $(X_1, X_2, X_3) \sim \text{Dirichlet} (\alpha_1, \alpha_2, \alpha_3)$
$\frac{Y_1 + ...
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Computation of ratio with Dirichlet distribution
I would like to compute ratio of proportions coming from a Dirichlet distribution. My understanding is that each proportion should be treated as a random variable and therefore I should use Taylor ...
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Advice on how to solve a constrained KL Divergence problem between a Dirichlet and a Logistic Normal
I would like some advice or path to follow to solve the following problem.
Consider a random variable $Y$ that follows a Dirichlet distribution $Y \sim Dir(\alpha)$. Let $X$ be a member of the ...
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How can we measure the "fit" between the softmax outputs and Dirichlet distribution?
For simplicity, I'll consider classification with 3 classes.
Then, softmax outputs can be considered as the set of points in 2-simplex.
I want to measure the 'fit' of this softmax output with target ...
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Ordinal regression - 'induced Dirichlet' conditional posterior distribution
I am trying to implement the 'induced Dirichlet' prior model proposed by Michael Betancourt (from section 2.2 of his ordinal regression case study here: https://betanalpha.github.io/assets/...
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Cross validation on bootstrap data
I am performing a dirichlet model for different species using a small sample size (between 8 to 20 samples per each).
Since my dataset is small, I bootstrap my data with 1000 iterations, averaging 3 ...
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Combining Dirichlet and Gamma-Normal distributions
I have a model that describes 2 dimensional data where each data points is define as d = [category, x].
The category dimension can take 3 different values with respective probability $p_1$, $p_2$ and $...
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Dirichlet Process posterior with partially observed data
Suppose I dipose of a set of independant observed couples $(x_1,y_1),...,(x_N, y_N)$ from a joint distribution $P(x,y)$. Furthermore, I suppose that the random distribution $P$ as a Dirichlet prior
$P\...
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Marginal density of dirichlet distribution
I'm studying BRML.
In this book, a Dirichlet distribution is defined as
$$
p(\alpha | u) = \frac{\Gamma(\sum_{q=1}^Q u_q)}{\prod_{q=1}^Q \Gamma(u_q)} \delta_0 \left( \sum_{q=1}^{Q} \alpha_q - 1 \right)...
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Comparing two randomly loaded dice
Say I have two six-sided dice, A and B, which are loaded in different ways, and I'd like to compare their probability distributions.
So far I've constructed the priors for the probabilities $\vec\pi = ...
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compute Dirichlet distribution parameter from known mean distribution
For a particular Bayesian study I am going to apply Dirichlet distribution as my proposal random number generator. I am going to update the distribution parameter every trial based on a given ...
