The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.

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Latent Dirichlet allocation: how to derive $\theta$ given $\alpha$?

I have been studying Latent Dirichlet allocation (LDA) since quite long. I have a confusion in Dirichlet priors. For example, if I consider 3 topics and take $\alpha_1 = 0.1$, $\alpha_2 = 0.1$ and ...
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which classifier to choose for probability histogram-like features

I have a populations of 500 elements. Each element is represented by a 10 dimension feature vector which sum of element is equal to 1 (you can think about it as a histogram of probabilities). In ...
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Dirichlet multivariable regression with temporal autocorrelation?

BACKGROUND: I have some animal behaviour data. The time allocated by a group of animals to different behaviours per minute was recorded repeatedly until the end of the experiment. Therefore, I have ...
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How can we plot realizations form a posterior distribution of a Dirichlet Process? What bin size to use?

In a Dirichlet Process, where $P \sim DP(\alpha P_0)$ and $y_i \sim P$ are iid, the posterior distribution of a Dirichlet Process $P$ is usually given as: $$ P \mid y_1, \ldots y_n \sim ...
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Is there any kernel defined for simplex domain (i.e. probability vector)?

I am wondering if there is any kernel function that is specifically designed for simplex domain. By "simplex domain," I mean a set whose elements are probability vectors. For example, 3-D simplex may ...
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Truncated Dirichlet process vs Dirichlet distribution

As the topic suggests I was wondering what the main differences are in using one over the other. Suppose for sake of simplicity the Dirichlet distribution has all parameters set to $\alpha$. All I ...
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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: http://mathoverflow.net/questions/20399/conjugate-prior-of-the-dirichlet-distribution ...
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63 views

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, ...
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Jeffrey's Prior for Dirichlet

As I understand, Jeffreys' Prior for any distribution is an objective one, and in the wiki, the Jeffreys' prior is written to be 0.5. On the other hand, I've found these notes which state that the ...
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23 views

Naive Bayes where Feature Space is LDA Output

I understand that the output for Latent Dirichlet Allocation is a distribution over K topics. Suppose I have a Dx(K+1) matrix, where rows are documents and columns are the topic distribution + one ...
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56 views

Probability of account win/loss using Bayesian Statistics

I am trying to estimate the probability of winning or losing an account, and I'd like to do this using Bayesian Methods. I'm not really that familiar with these methods, but I think I understand the ...
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56 views

Dirichlet Distribution with constraints

This is a follow up to an earlier question that I asked here: How should I measure my confidence in this estimate of this finite distribution In that question I asked how I could estimate a finite ...
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How to fit a Dirichlet Process prior?

I currently am working with the galaxies dataset in the R package "DPpackage". I am trying to assume that each of my datapoints $y_i \sim P$ with $P \sim DP(\alpha P_0)$, which denotes a Dirichlet ...
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Modelling distributions evolving with time

Say we have N probability vectors of dimensionality D describing how a process evolves in N time steps, something like multidimensional time series. What's the best way to model this sequence in ...
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296 views

Why doesn't PDF of Dirichlet Distribution seem to integrate to 1?

I have been trying to find the expected value of a function of a random variable with a Dirichlet distribution by integrating its product with the Dirichlet density function over a simplex in R. To ...
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27 views

Marginal probability function of the Dirichlet-Multinomial distribution

I can't seem to find a written out derivation for the marginal probability function of the compound Dirichlet-Multinomial distribution, though the mean and variance/covariance of the margins seem to ...
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What is the mode of the Dirichlet distribution when some $\alpha_i < 1$

Suppose $X \sim \mathcal D(\alpha_1, \ldots, \alpha_p)$, and suppose $\alpha_i < 1$ for some $\alpha_i$. In this case, the density is unbounded, and so no proper "mode" can exist. On the other ...
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Sampling of dirichlet distribution complexity

What is time complexity of sampling of a dirichlet distribution with size N? Thanks
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43 views

Generate data from Dirichlet distribution? [closed]

I want to generate Dirichlet distributed data, but I don't know how to do it. Could you please help me?
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31 views

Polya Urn - formulas

i am trying to understand Dirichlet processes and Polya's Urn, following the excellent article ...
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dirichlet process - formula explanatation

i am self-studying the Dirichlet process, from among others http://www.stat.ubc.ca/~bouchard/courses/stat547-sp2011/notes-part2.pdf, and struggling with the following basic question: I understand ...
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44 views

About LDA model, I need a true expert to tell me that what is the real benefits of the Dirichlet prior? [closed]

Well,you know ,the only difference between pLSI and LDA is that the latter has a Dirichlet prior,thus the number of model parameters do not increase with the size of corpus,and this avoid the ...
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65 views

Where to find Wikipedia's wiki.dat for LDA, an example used in Vowpal Wabbit? [closed]

I am following Vowpal Wabbit's tutorial on LDA (Latent Dirichlet Allocation) found here. wiki.dat is used in it as a Wikipedia corpus or supplementary Wikipedia dictionaries, maybe. It must be ...
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Distribution of the largest fragment of a broken stick (spacings)

Let a stick of length 1 be broken in $k+1$ fragments uniformly at random. What is the distribution of the length of the longest fragment? More formally, let $(U_1, \ldots U_k)$ be IID $U(0,1)$, and ...
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Gaussian mixture models and Dirichlet Processes - choosing alpha

Can someone point me to a good empirical method or rule of thumb for choosing alpha in a Dirichlet Processe mixture? (Alpha as outlined here: ...
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Simplification of the marginalized multinomial distribution

The likelihood expression for multinomial count variables $\{n_1, \dots, n_K\}, \sum_{k=1}^K {n_k} = N$, conditionned by parameters $\{\pi_1, \dots, \pi_K\}, \sum_{k=1}^K {\pi_k} = 1$ is given as: ...
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Uniform Sampling from Intersections of Faces of Simplices

I'm trying to sample uniformly on the intersections of faces of several simplicies, with all coordinates being non-negative. That is, given constraints $$A\vec{w}=\vec{b} \ \ and \ \ \vec{w} \geq ...
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Dirichlet predictive distribution

I need to derive a posterior predictive density for observation T+1 given that the posterior distribution of $(x_{1}, x_{2}, 1-x_{1}-x_{2})$ is a Dirichlet distribution with parameter $(\alpha_{1}, ...
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What is the median of the Dirichlet Distribution?

The Dirichlet is a multivariate generalisation of the Beta distribution, and Wikipedia states that the median of the Beta distribution is the inverse of the incomplete Beta function evaluated at ...
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Material on plate notation of bayesian hidden markov model

Does any one know some materials on plate notation of Bayesian Hidden Markov Model? Say, given multiple observed sequences, how to infer the posterior distribution of the parameters, and the ...
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How to sample from a distribution while the sample point simultaneously needs to satisfy an inequality constraint?

I have a Dirichlet distribution $P(x)$ , where $x$ is a point on a simplex. It is very easy to sample from this Dirichlet distribution. But I have a set of non-linear, non-convex constraints ...
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58 views

Multinomial distribution - where is the normalising constant?

I've been reading up on Multinomial/Dirichlet priors and came across this note. I'm wondering why the normalising constant for the multinomial distribution drops out in the derivation of the joint ...
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75 views

How to simulate a multivariate Logistic-Normal distribution in Python

I'm trying to generate a text document using reverse "Correlated Topic Models", which is an advanced version of LDA (Latent Dirichlet Allocation). In this version the topics are generated over a ...
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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 ...
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Alpha Parameter Specification Dirichlet Prior

I have a straightforward Dirichlet-Multinomial model with code that is running in RJAGS. The data are a collection of 200 2 x 2 contingency tables. The multinomial counts are those of a 2 x 2 ...
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Can a Multinomial(1/n, …, 1/n) be characterized as a discretized Dirichlet(1, .., 1)?

So this question is slightly messy, but I'll include colourful graphs to make up for that! First the Background then the Question(s). Background Say you have a $n$-dimensional multinomial ...
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247 views

Sampling from Dirichlet-Multinomial

How do I sample from a Dirichlet-Multinomial distribution. One which has this pmf: http://en.wikipedia.org/wiki/Dirichlet-multinomial_distribution#For_a_multinomial_distribution_over_category_counts
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How to interpret the coefficients from Dirichlet Regression?

I have a response Y, which consists out of 5 response variables which are proportions and for each observation, add up to 1. I'm tying to regress these with a set of independent variables. As I ...
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514 views

RJAGS Multinomial-Dirichlet – Observed node inconsistent with unobserved parents at initialization

I am trying to model a simple 2x2 contingency table with a multinomial-Dirichlet model. A snippet of my data z[i,1:4] look like this: ...
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Estimating parameters of Dirichlet distribution

This is a very basic question but after reading few documents I found online I am a bit confused about Dirichlet parameter estimation. My data is multinomial. I have my Dirichlet prior and I would ...
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Generating column stochastic random matrix with target row sums

I want to populate a 0-1 matrix, which is an adjacency matrix, corresponding to a directed graph, with weights on the elements that are 1. In other words, I want to generate an $N\times N$ matrix $A$ ...
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Variance of multinomial distribution that is product of 4 Beta random variables

I have a system of 4 binary random variables, $A$, $B$, $C$ and $D$. $A$, $B$ and $C$ are conditionally independent given $D$, and I'll call one set of samples $ABCD$ an event (e.g. $ABCD$ meaning all ...
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Is this a true inequality over multinomial parameters?

Let $p_1,\ldots,p_k$ be the multinomial parameters sampled from a Dirichlet distribution. Assume $\bar{p_1},\ldots,\bar{p}_k$ be the mean of Dirichlet distribution. Then, $$Pr( ...
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Is it possible to define the mean of a varying distribution?

Suppose $(p_1,\ldots,p_k)$ be the vector of multinomial parameters and $$(p_1,\ldots,p_k)\sim \mbox{Dirichlet}(\alpha_1,\ldots,\alpha_k).$$ Let's define a function $f(p_1,\ldots,p_k) \in \mathbb{R}$. ...
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158 views

Hierarchical Dirichlet Processes in topic modeling

I think I understand the main ideas of hierarchical dirichlet processes, but I don't understand the specifics of its application in topic modeling. Basically, the idea is that we have the following ...
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Simulating r.v.'s $X, Y, X \in [0,1]: X+Y+Z = 1\;a.s.$ given we know $E[X],E[Y],E[Z]$ and $E[X]+E[Y]+E[Z]=1$ with marginal variances $\sigma^2$

I think my title says most of my question, but let me re-state: I am trying to simulate variable percentages (i.e., X,Y,Z) on the above simplex without using the Dirichlet distribution. The reason ...
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Maximum Likelihood Estimation of Dirichlet Mean

Consider the problem of computing a Maximum-Likelihood estimate of the parameters to a finite Dirichlet distribution, given a set of multinomial observations (probability vectors) assumed to have been ...
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What is a Dirichlet prior

I am doing some bioinformatics research but my background is Applied Math and I usually have trouble with the statistics part of it. Basically, I've created a Position Weight Matrix using a R ...
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Looking for invariants to test the implementation of the Dirichlet distribution

We have implemented the Dirichlet distribution (in Smalltalk) and are looking for ideas on how to test our versions of the cdf and pdf functions. One idea that comes to mind is to compare the results ...
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419 views

How do you estimate $\alpha$ parameter of a latent dirichlet allocation model?

Blei has shown that it is possible to estimate $\alpha$ in a LDA model, but I have yet to find a library (any library; C, C++, Java, ...) to do so. Usually, implementations (including Blei's) treat ...