All Questions
Tagged with dirichlet-distribution distributions
52
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What is a representation of positive numbers summing to one that can be sampled via HMC?
I have a probability density $f(x): \mathbb{R}^n \rightarrow \mathbb{R}$ whose argument vector $x$ satisfies the constraints that all elements are positive and sum to unity. I need to generate samples ...
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1
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143
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Choosing a probability distribution for 4D data: dirichlet challenges and alternatives
I'm seeking the right distribution for my 4D data, where the sum of values in each sample equals one. Currently, I've chosen to employ the Dirichlet distribution. However, upon applying this ...
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Do you know if this re-scaled Dirichlet kernel is known in the literature? How to sample from it?
In a Bayesian analysis, I came across the following distribution that results ends up looking like a re-scaled Dirichlet distribution. The motivation comes from looking at probabilities $x_1, \ldots, ...
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41
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A confusion about computing transformation of random variables
Let $(X,Y)$ be a pair of random variables with joint pdf $f_{XY}$. Let $(U,V)$ be two random variables obtained from $(X,Y)$ by $U = u(X,Y)$ and $V = v(X,Y)$ where $u$ and $v$ are, say, nice ...
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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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2
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376
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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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Mixtures of Dirichlet multivariates or Dirichlet processes
I am exploring the properties of Dirichlet distributions and their parameters. When mixing two Dirichlet distributed random bivariates
$$\mathbf{X}\equiv(X_1,X_2)\sim\text{Dir}(\alpha_1,\alpha_2)$$
...
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129
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Dirichlet distribution parameters from known variances
Let's assume, I know the variances of Dirichlet distribution parameters. Let these variances be:
$Var[X_1], ..., Var[X_n]$.
Is there a analytical solution to derive the parameter value alpha_i given ...
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2
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217
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Sum of squares for a Dirichlet distribution
I have some data that takes the form of vectors $(a_0,...,a_n)$ lying on the simplex $\Sigma a_i = 1$ (all $a_i$'s non-negative). I have noticed that the maximum $\max_i a_i$ is very highly correlated ...
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187
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Using the methods of moments in R for the dirichlet distribution
I'm trying to build a distribution of transition probabilities to randomly sample from in a Markov model where individuals can transition from one health state to another (assume that in the image ...
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456
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Approximating the Logit-Normal by Dirichlet
There is a known approximation of the Dirichlet Distribution by a Logit-Normal, as presented in wikipedia.
However, I am interested in the reverse, can I approximate a logit-normal by a Dirichlet?
I.e....
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814
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How to generate data from a generalized Dirichlet distribution?
I need to generate data from a generalized Dirichlet distribution in Python to test my model, but I have no idea how can I proceed with that, can anyone guide me?
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How to visualize Dirichlet distribution (with more than 3 targets)?
I want to plot a Dirichlet distribution $\operatorname{Dir}(\alpha), \alpha=[\alpha_1, \alpha_2, \ldots,\alpha_n]$. However, when I google it, almost all of the results consider 3 targets ($n=3$), and ...
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On the distribution of a scaled sum of a Dirchlet random variable
Consider $(X_{1},\dots,X_{K})=X\sim \text{Dir}(\alpha)$ and a vector $v=(v_{1},\dots ,v_{K})\in\mathbb{R}^{K}$.
Is there a parametric density function for the distribution of:
$Xv^{T}=vX^T=\sum^{K}_{i=...
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