The dirichlet-distribution tag has no wiki summary.
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30 views
Categorical value “stuck” during sampling of my model
I'm having some troubles with the implementation in pyMC of my probabilistic model.
Note: you can skip directly to the code section, if you're not interested on the use of the model.
The model ...
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1answer
38 views
Dirichlet multinomial for adverse event data
I am trying to see which distribution will best fit the data I am working on. The dataset is as following:
...
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2answers
103 views
Implementation of Dirichlet cdf?
I need to compute the Dirichlet CDF, but I can only find implementations of the PDF.
Do you guys know of any library (preferably in R) implementing it?
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0answers
38 views
Understanding the construction of Dirichlet process
I'm trying to understand the construction process of DP, however, with little background in measure theory, the original papers are hard to read, but I believe the ideas behind these papers can be ...
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1answer
61 views
Derivation of the posterior over topics in LDA
When studying the latent Dirichlet allocation, I am not very clear about some procedures in their deriving equations. Please refer to the attached figure, how to understand those two steps, marked as ...
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1answer
75 views
Multivariate proportional data
I am looking for literature on what I call multivariate proportional data where a single observation is a vector of proportions that sum to 1. For example, each person weights their preferences for ...
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2answers
166 views
Bayesian estimation of Dirichlet distribution parameters
I want to estimate parameters of Dirichlet mixture models using Gibbs sampling and I have some questions about that:
Is a mixture of Dirichlet distributions equivalent to a Dirichlet process? What ...
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0answers
36 views
How to find the MLE for two dirichlet distribution with same mean
I have samples from two groups. Samples from each group follow a Dirichlet distribution. The two Dirichlet distributions have the same mean but different precision. How to find the MLE of mean and two ...
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2answers
101 views
kernel density estimation of a Dirichlet distribution
I have a Dirichlet distribution over the parameters of a multinomial, and I want to estimate its posterior density given some set of evidence. Due to some pecularities of my problem (e.g. presence of ...
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1answer
96 views
Latent Dirichlet analysis document comparison
I have been using Latent Dirichlet Analysis for a while but I am a bit confounded as to it's practical ability to compare two documents. It is of course ideal for classification when you want to see ...
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2answers
134 views
Bayes Estimation on Dirichlet distribution
I'm trying to get my head around the "hidden species" problem. It goes something like this. You visit a park and run into three species, 3 lions, 2 tigers and 1 bear. You are to determine what is your ...
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1answer
89 views
Nonparametric Topic Models
I am confused between what types of problems these three models capture, and their applications:
Latent Dirichlet Allocation (LDA)
Dirichlet Processes and Pitman-Yor processes
Hierarchical Dirichlet ...
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1answer
164 views
Latent Dirichlet Allocation (LDA): What exactly is inferred?
I am working my way through LDA and I think I got they main idea of it. Please correct me if I am wrong. Given the Plate notation:
The variables $\alpha$ and $\beta$ are Dirichlet distribution ...
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2answers
540 views
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 Multinational as a pair?
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2answers
260 views
Multinomial-Dirichlet model with hyperprior distribution on the concentration parameters
I will try to describe the problem at hand as general as possible. I am modeling observations as a categorical distribution with a parameter probability vector theta.
Then, I assume the parameter ...
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1answer
53 views
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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1answer
125 views
Dirichlet posterior
I have a question about the Dirichlet posterior distribution. Given a multinomial likelihood function it's known that the posterior is $Dir({\alpha_i + N_i})$, where $N_i$ is the number of times we've ...
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1answer
144 views
Calculating Log Prob. of Dirichlet distribution in High Dimensions
I'm interested in calculating the log probability of data drawn from a Dirichlet distribution. In particular, I'm interested in calculations that are stable in high dimensions, perhaps 1000 dimensions ...
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315 views
Construction of Dirichlet distribution with Gamma distribution
Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that ...
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1answer
107 views
Distributions on the simplex with correlated components
I'm looking for some kind of distribution over the simplex in which components are correlated in an ordinal way. That is, if $p = (p_1, ..., p_J)$ is drawn from our distribution on the simplex, I ...
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41 views
Dirichlet density with just one x value and one alpha parameter
Does it make any sense to apply the Dirichlet density function to only one x value and therefore one alpha parameter? (this would be the result of some bin merging)
I'm asking because it appears ...
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22 views
dirichlet density function returning values > 1.0 [duplicate]
Possible Duplicate:
Probability distribution value exceeding 1 is OK?
I'm comparing results given by this implementation and that from the gtool library in R, of the Dirichlet density ...
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1answer
146 views
Input parameters in Dirichlet density function
I'm trying to feed the Dirichlet density function with some sample data and estimated alpha vector using R in Python (library rpy2), but I don't understand the error that I got:
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3answers
483 views
Mixture Models and Dirichlet Process Mixtures (beginner lectures or papers)
In the context of online clustering, I often find many papers talking about: "dirichlet process" and "finite/infinite mixture models".
Given that I've never used or read about dirichlet process or ...
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1answer
182 views
Proposal for transition matrix for Metropolis-Hastings phylogenetic inference
I am using the Metropolis-Hastings algorithm for phylogenetic inference. To do so I would like to draw the substitution matrix Q from the generalized time-reversible model.
To do so I need proposal ...
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3answers
564 views
Simple introduction to MCMC with Dirichlet process prior?
I'm looking for a simple and easy to read introduction to using MCMC with a dirichlet process prior. Or perhaps using MCMC in any machine learning scenario, eg Gaussian Process.
I've been circling ...
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1answer
489 views
The input parameters for using latent Dirichlet allocation
When using topic modeling (Latent Dirichlet Allocation), the number of topics is an input parameter that the user need to specify.
Looks to me that we should also provide a collection of candidate ...
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83 views
Most used name for Dirichlet Compound Multinomial dist (aka Dirichlet-Multinomial, Multivariate Polya)?
I'm doing a lot of work on the Wikipedia page for this distribution:
http://en.wikipedia.org/wiki/Dirichlet_compound_multinomial_distribution
The actual name of the page is "Multivariate Pólya ...
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2answers
341 views
Generating from Dirichlet distribution with the differences in a sequence of ordered uniform
First, let's assume that we want to generated from a Dirichlet(1,1,1,1) distribution. Would the following method be correct?:
generate three variates from a Uniform(0,1). Call them $x_1$, $x_2$, ...
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1answer
905 views
Dirichlet distribution plot in R
I want to plot $15$ random draws of Dirichlet distribution with $\alpha = 1$ and dimension $n=10$ in R.
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0answers
159 views
$\chi^2$ test for data from Dirichlet-multinomial distribution
Suppose I am given $n$ samples of sizes $N_1, \dots, N_n$ from a Dirichlet–multinomial distribution: Fixed and given is a $k$-vector $\mathbf{\alpha}$ of positive real numbers. For each $i, \, 1 ...
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1answer
488 views
Bayesian inference for multinomial distribution with asymmetric prior knowledge?
Suppose I will be getting some samples from a binomial distribution. One way to model my prior knowledge is with a Beta distribution with parameters $\alpha$ and $\beta$. As I understand it, this is ...
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1answer
365 views
What is the expected value of modified Dirichlet distribution? (integration problem)
It is easy to produce a random variable with Dirichlet distribution using Gamma variables with the same scale parameter. If:
$ X_i \sim \text{Gamma}(\alpha_i, \beta) $
Then:
$ ...
