All Questions
Tagged with dirichlet-distribution beta-distribution
18
questions
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68
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How to calculate the expectation of the following Dirichlet distribution and Beta distribution?
This is a question from my research, related to the derivation of the variational EM algorithm with mean-field assumption about LDA-based model.
We all know, given that $\boldsymbol{\theta} \sim \...
- 11
1
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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
2
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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
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200
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How is a convex combination of Dirichlet-distributed variables distributed?
Let $X = (X_1, \dots, X_K) \sim \operatorname{Dir}(\alpha_1, \dots, \alpha_K)$ and define the convex combination $Y = \sum_{i=1}^{K} c_i X_i$.
In the case of $K=2$, the constraint $\sum_{i=1}^{K} X_i =...
- 31
3
votes
1
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146
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Bayesian (continuous) logistic regression model with Beta likelihood?
I have a problem where my target variable are continuous/float values in the range [0,1]. If my data were integers in {0,1} this would be a simple logistic regression / Bernoulli likelihood problem. ...
- 3,382
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174
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Dirichlet-distribution and its correlation?
I have the following variables that follow a beta distribution:
...
2
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34
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Proving independence relationship
Let $X_1,X_2,X_3$ be continuous positive random variables satisfying $X_1+X_2+X_3<1$ and the following independence relations
$$\frac{X_1}{X_1+X_2}\perp \!\!\!\perp \frac{X_3}{1-X_1-X_2}~ and$$
$$\...
- 433
6
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638
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Aggregation with an overlap: Dirichlet distribution
Suppose that we have $$(p_1,p_2,p_3,p_4)\sim Dirichlet(a_1,a_2,a_3,a_4),$$
where $p_4=1-p_1-p_2-p_3.$
When we add random variables for example, $p_1+p_2$ and $p_3+p_4$, the resulting distributions ...
- 433
2
votes
2
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2k
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Bayesian update for Beta distribution
I'm wondering how to find a posterior of a beta distribution when the "new information" is not an outcome of a binomial trial.
Let $p$ be the probability of Head of a (biased) coin toss. As usual in ...
- 433
3
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1
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1k
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From beta distribution to Dirichlet: Estimation of the concentrantion parameters
Searching at least 3 hours about the connection between beta distribution and dirichlet. My problem is:
I have a collection of random variables $X_i \sim Beta(a_i, b_i)$. The parameters $a_i$ and $...
- 163
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245
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Is fair to compare Dirichlet to a Multivariate Beta regression?
I am conducting some analysis on my data I found a strange behavior and would greatly appreciate some guidance or suggestions.
I am trying to investigate the effect of a categorical variable (cl) to ...
3
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498
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How to specify a zero-inflated Dirichlet model in JAGS/BUGS
There was a recent publication discussing the advantages of the zero-inflated dirichlet for microbiome count data which is compositional (you are modeling a matrix of species relative abundance data ...
- 1,242
1
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1
answer
912
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Trouble specifying a hierarchical dirichlet model in JAGS
I have a sampling design where samples (cores) are taken within plots. Those plots are then nested within sites. There are multiple sites. I would like to get a hierarchical site-level estimate of ...
- 1,242
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113
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Marginal medians of the Dirichlet distribution
I am working with a 3 dimensional Dirichlet distribution with parameters $\alpha_1,\alpha_2,\alpha_3>0$. I have been trying to figure out a useful 'median' concept for this distribution. The vector ...
- 41
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401
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Covariance between X and ln(Y) with X and Y beta random variables
I have a Dirichlet distribution $D(\alpha_1,\alpha_2,\alpha_3)$, with $\alpha=\sum_{i=1}^3 \alpha_i$. I know that the marginal distributions are beta distributions. Consider for instance the first 2 ...
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