All Questions
Tagged with dirichlet-distribution probability
31
questions
1
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0
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65
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Power of Uniform Order Statistics
I know that if $U$ is a uniform r.v. in $(0,1)$, then $U^a\sim Beta(1/a,1)$ with $a>0$.
On the other hand, if $U_{(1)}\leq \cdots\leq U_{(n)}$ are the uniform order statistics, then, with $U_{(0)}=...
- 111
1
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0
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139
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Stick-breaking construction of Dirichlet distribution vs Dirichlet process
Let $F_0$ be some probability measure and $\alpha > 0$ be the concentration parameter. I can draw a random distribution from $F\sim \mathrm{DP}(\alpha, F_0)$ using the stick-breaking construction:
\...
- 183
2
votes
1
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92
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Interpreting the quantities sampled from a Dirichlet distribution
Suppose you sample $M$ vectors from $Dirichlet_K(\alpha)$. You then show a histogram summarizing the distribution of the $M$ values that were sampled for dimension $k = 1$ (i.e. the first dimension, ...
- 847
1
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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 ...
0
votes
0
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174
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Dirichlet-distribution and its correlation?
I have the following variables that follow a beta distribution:
...
1
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0
answers
61
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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=...
- 11
3
votes
0
answers
80
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Bounding values of a Dirichlet distribution
Consider $k$ random variables $X_1, X_2, \ldots, X_k$ such that $(X_1, X_2, \ldots, X_k)$ follow a $\text{Dirichlet}(1, 1, \ldots, 1)$ distribution. For a large enough $k$, I am trying to bound/find ...
- 247
0
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2
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41
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What Distribution Do I need?
Suppose I am drawing coloured balls from a bag.
The ball can be red, green or blue.
The probabilities of drawing a red, green or blue bag are uncertain, but I have confidence bounds for the ...
- 35
-1
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1
answer
160
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I want to represent x1, x2, ..., xn (where their sum =1) by Dirichlet distribution. What alpha's should I select if x1, x2,... have the same pdf
I want to represent x1, x2, ..., xn (where their sum =1) by Dirichlet distribution. What alpha's should I select if x1, x2,...,xn have the same probability density function? all 0 < xi < 1. In ...
- 143
3
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2
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373
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Probability that a random variable is smaller than another in a random vector
Suppose that a random vector $X=(X_1,X_2,X_3)$ follows a Dirichlet distribution with a shape parameter $(a_1,a_2,a_3).$
What I want to calculate is the probability of $X_1>X_2$ and I want to ...
- 119
0
votes
1
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230
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Definition of distribution conditioned on both a categorical and Dirichlet prior
If we have a conditional categorical distribution, with unknown parameters, we can represent with a table, as in the example below:
\begin{align*}
&z \quad P(z|\theta)\\
&0 \quad \theta_0\\
&...
- 191
2
votes
1
answer
568
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Normalization constant for uniform distribution over categorical distributions
Suppose we have a uniform distribution over all categorical distributions p for m categories, where the pdf has the form
$$
f(x) = \left\{\begin{aligned}
&c, && 0 \le p_i \le 1, i = 1, ......
- 161
2
votes
0
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229
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Calculate Variance from Dirichlet-like Distribution Empirically
I'm interested in the proportion of time that a sensor is in a particular state. The sensor tells me the amount of time that it's in each state, which I will denote by $X = \{ X_1, X_2, X_3\}$. I ...
- 675
1
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0
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269
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Entropy of Dirichlet distributed vector
Suppose I have two Dirichlet distributed vectors $X$ and $Y$ such that $ X \sim \text{Dirichlet}(\alpha) $, $ Y \sim \text{Dirichlet}(\beta) $ with fixed vectors of hyperparameters $\alpha$ and $\beta$...
2
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0
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73
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Is 1 - Dirichlet variable also a Dirichlet?
Just a simple question regarding the properties of Dirichlet distribution:
Suppose $(X_1, \ldots, X_K) \sim Dir(\alpha_1, \ldots, \alpha_K)$, can we express the distribution for $(1-X_1, \ldots, 1-...
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