All Questions
Tagged with dirichlet-distribution conjugate-prior
15
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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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1
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Why use MCMC sampling when using conjugate priors?
I've been getting to grips with some Bayesian modelling, but one thing is confusing the heck out of me when I look at tutorials and worked-through problems online. I'm looking at a problem with a ...
- 121
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How to use the Dirichlet prior for estimating the multinomial parameters? [closed]
I know that the multinomial distribution gives the likelihood of some vector D of occurrences to happen given a probability vector (parameters) P' i.e. P(D|P'). Now with a Dirichlet prior we are ...
- 272
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Predictive Density for Dirichlet Multinomial
I am wondering what the predictive distribution of a Dirichlet-Multinomial distribution is.
In this tutorial (page 24), the predictive density is simple and something like "pseudo samples."
However, ...
- 678
3
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Sampling from conjugate Dirichlet distribution
Conjugate prior for Dirichlet distribution, as described by Lefkimmiatis, Maragos, and Papandreou (2009; see also here and here), has form
$$
f(\boldsymbol{\alpha}) \propto \frac{1}{B(\boldsymbol{\...
- 140k
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Variance of multinomial and Dirichlet-multinomial distributions
I have an application where I would like to sample from a multinomial distribution, but I am concerned that the variance will be too low. As an alternative, I am considering the Dirichlet-multinomial ...
- 421
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what is this property? $\int p(x,\pi)d\pi=p(x|E[\pi])$?
Sorry if the title does not make sense, from the answer of this question Mistake in derivation about categorical distribution and Dirichlet distribution? it can be shown that
say $p(x|\pi)$ follows ...
- 16.6k
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380
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Mistake in derivation about categorical distribution and Dirichlet distribution?
$p(x|\pi)$ follows the categorical distribution (the multinomial with one observation), where $\sum\pi_i=1$ and $x$ is a one-hot vector, and $p(\pi|\alpha)$ follows the Dirichlet distribution.
$p(x|\...
- 16.6k
8
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3
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Dirichlet conjugate update derivation
I am attempting to derive the update equations for the conjugate to the Dirichlet distribution, as outlined here: https://mathoverflow.net/questions/20399/conjugate-prior-of-the-dirichlet-distribution
...
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7
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Dirichlet Prior for Multinomial
The Dirichlet function is the conjugate prior of the multinomial.
So the posterior is also Dirichlet given some observations.
If e.g. I observe the counts $X=(10,3,4)$ from 17 trials (10 for class 1, ...
- 682
2
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Conjugate prior to a Dirichlet sample distribution? [duplicate]
The Dirichlet distribution is the conjugate prior to the multinomial sampling distribution. What is the conjugate prior (if any) if the sampling distribution is itself Dirichlet? That is, our ...
- 123
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538
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can Dirichlet prior distribution be larger than 1?
This question is related to my quest of clustering the sequences using mixture Markov modeling.
I have trouble understanding Dirichlet priors in the context of MAP-estimate (Mixture Markov Models). ...
- 779
1
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1
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How to use prior probability in inferencing from HMM for activity recognition?
I am interested in modelling human activities using sensor data with HMMs and would like to incorporate prior knowledge during inference. The normal procedure is to model K different activities with K ...
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39
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Why is the Dirichlet distribution the prior for the multinomial distribution?
In LDA topic model algorithm, I saw this assumption. But I don't know why chose Dirichlet distribution? I don't know if we can use Uniform distribution over Multinomial as a pair?
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Any actual applications based on "dirichlet distribution servers as a conjugate prior for multinomial distribution"
Conjugate prior is useful and beautiful in theory, for instance, Dirichlet distribution can serves as the conjugate prior for multinomial distribution. But I don't find any actual applications based ...
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