All Questions
Tagged with dirichlet-distribution posterior
12
questions
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66
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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\...
- 11
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1
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187
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Uniform posterior on bounded space [duplicate]
In a particular Bayesian problem, I have encountered a choice of parameters that leads to a uniform posterior distribution. Given prior
\begin{equation}
p(\boldsymbol{\pi}) =Dirichlet(\boldsymbol{\...
- 655
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1
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1k
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Bayesian posterior pmf for weighted dice with uniform prior
We want to find posterior probability mass function for dice tossing with uniform prior.
We are interested in rolling of weighted dice. The outcome is 1,2,...,6.
We assume that prior probability ...
- 3
1
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1
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2k
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Maximum a posteriori on Multinomial distribution with a Dirichlet prior can result in negative probabilities?
I am doing a maximum a posteriori (MAP) estimation of a Multinomial distribution $M(c_1,\dots,c_n|p_1,\dots,p_n)$ with a Dirichlet prior $D(p_1,\dots,p_n|\alpha_1,\dots,\alpha_n)$. The experimental ...
- 113
2
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1
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2k
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Posterior mode, posterior mean and posterior variance of a posterior distribution of dirichlet form
What is the significance of finding the posterior mean, posterior mode and posterior variance in Dirichlet - multinomial conjugate pair Bayesian estimation? Are all of them equally important while ...
1
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0
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101
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For Latent Dirichlet Allocation, why is setting alpha to a very low value equivalent to having a mixture model?
I'm watching a video on topic modeling by David Blei (from 27:00 of Part 2) and I don't understand how setting the $\alpha$ hyperparameter to a value close to zero basically results in a mixture model ...
- 111
4
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1
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912
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Posterior of Dirichlet distribution parameters
I want to obtain posterior distribution for parameters of a Dirichlet distribution $x = (p_1,p_2,p_3) \sim Dir(p_1,p_2,p_3; a_1,a_2,a_3)$ with uniform $P(a_1,a_2,a_3)$ and observed data $X=\{x_1,x_2,.....
- 205
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3
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1k
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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
...
- 89
3
votes
1
answer
416
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Variational Posterior Dirichlets in LDA
I am running the c code for LDA provided on David Blei's website. The code outputs several files. The output file final.gamma is supposed to include the "Variational Posterior Dirichlets". If I ...
- 135
3
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1
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302
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Latent Dirichlet Allocation - understanding the posterior
I have a problem understanding the posterior for computing LDA, stated in page 7 of Blei (2007). From my point of view, it's not exactly consistent with Bayes' theorem, as described here. Could anyone ...
- 1,309
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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 ...
- 33
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179
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Posterior in latent Dirichlet analysis
I have a question regarding LDA (Latent Dirichlet Analysis) - what is the correct formulation of the posterior? In http://www.cs.princeton.edu/~blei/papers/Blei2011.pdf it is $p(\beta_{1:K}, \theta_{...
- 1,309