All Questions
Tagged with dirichlet-distribution mathematical-statistics
11
questions
0
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13
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Mapping two Dirichlet Distributions into a comparative Dirichlet
Assume I observe some draws from 2 choice options, and want to infer the probabilities of various outcomes, e.g. non-negative integers up to a limit L. I could simply use 2 Dirichlet distributions to ...
- 23
1
vote
0
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72
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Zero-Inflated Dirichlet
I want to set up a model that will rely on something similar to a zero-inflated Dirichlet distribution. As such, I'm trying to figure out how a zero-inflated Dirichlet distribution is set up from the ...
- 225
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34
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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, ...
- 93
1
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0
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97
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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 ...
- 76
1
vote
1
answer
96
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Concentration Bounds for categorial distribution with good Dirichlet prior
I would like to know if there are any standard methods for analyzing the concentration bounds (for example Hoeffding's bound) for a multinomial distribution modelled with a Dirichlet prior, with the ...
- 131
4
votes
1
answer
1k
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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 ...
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
1
vote
0
answers
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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1
answer
1k
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Bayesian smoothing using Dirichlet prior : why not MAP?
I am reading about smoothing methods for language model ( I am working on unigram model).
If you are not familiar with unigram model, it is closely related to multinomial distribution (with the ...
- 57
4
votes
1
answer
547
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L1 distance between Dirichlet distributions
Given two Dirichlet distributions $\mu_{\alpha},\mu_{\beta}$ on the k-simplex, with parameters
$\alpha = (\alpha_1,\ldots,\alpha_k)$ and $\beta = (\beta_1,\ldots,\beta_k)$, is there an expression for ...
- 103
4
votes
1
answer
4k
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stick breaking model of Dirichlet process
I have a question regarding sticking-breaking model of Dirichlet process, which is defined as follows:
There are further statements that
I am not clear that how to derive equation 1 from that ...
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