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

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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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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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34 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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115 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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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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46 views

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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93 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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66 views

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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130 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 ...
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What is the intuition behind Dirichlet distribution?

looking for explanation on similar lines What is the intuition behind beta distribution?
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Can dummy variables be used to represent space in latent Dirichlet allocation?

Can dummy variables be used to represent space in latent Dirichlet allocation? I have a set of geocoded textual documents. I would like to use LDA to generate a topic model for the documents. ...
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Comparing support of Dirichlet

If (x1, x2, x3, x4) ~ Dirichlet(a1, a2, a3, a4), find P(x1 > x2)? I tried to use integration, but it didn't work out... Could anyone please provide any help? I greally apprecaite it!!
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59 views

What is a draw from a Dirichlet Process?

I know a draw from a K-D Dirichlet distribution is a probability vector of dimension K. But still it's not clear what is a draw from a Dirichlet Process. What I understood is that a draw from a ...
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164 views

PyMC3 Dirichlet Distribution

I am implementing a linear regression model in pymc3 where the unknown vector of weights is constrained to be a probability mass function, hence modelled as a Dirichlet distribution, as in the ...
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Recursively computing Dirichlet cdf.

I want to implement the Dirichlet CDF and I wonder if I can compute it recursively Following Frigyik et al., we know that if $Q \sim \text{Dir}(\alpha)$, then: $X_1 \sim \text{Beta}(\alpha_1, ...
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72 views

Draw a multinomial distribution from a Dirichlet distribution?

I have a very rough understanding of the Dirichlet distribution and already seen some visualizations of its pdf over the 2-simplex, i.e., $\alpha$ is a 3D vector. However, I still do not understand ...
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148 views

Simulation from Dirichlet distribution with WinBUGS

I have a question. Now I am learning WinBUGS, doing bayesian statistics. How, can I simulate a Dirichlet distribution (which is the posterior, for my model ...
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134 views

Dirichlet process mixture model in Python

My question is concerned with the practical issues of using this model. I've tried to use Dirichlet process mixture model from Scikit learn python package to find a number of clusters in my data (1D ...
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multivariate dirichlet for multiple imputation

I dealing with 3 covariates {x1, x2, x3} all three are discrete and contain missing data. ...
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For inference of Dirichlet Process Mixture, why the expected value $\int h(x)f(x)$ is desired?

Why the expected value $\int h(x)f(x)$ is desired for inference in Dirichlet Process Mixture? What is the intuition for MCMC in Dirichlet Process Mixture? $f(x)$ is the probability density function, ...
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Finite mixture models - Basic understanding

I have been reading lecture slides about Dirichlet Process. In page 22, there is a picture about the following finite mixture model. $$\phi _{k}\sim H\\ \pi \sim Dirichlet(\alpha /K,\dots,\alpha ...
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Expectation of a generalization of Dirichlet distribution

For the standard Dirichlet, the expectation of $X_i$ is $\alpha_i/\alpha_0$, where $\alpha_0 = \sum_i \alpha_i$ (http://en.wikipedia.org/wiki/Dirichlet_distribution). I am considering the following ...
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Dirichlet sample by normalising Gamma RVs

I know that if you sample $K$ random variables $(X_1, X_2, \dots, X_K)$ from Gamma distributions using shape parameters $(\alpha_1, \alpha_2, \dots \alpha_K)$ and a scale parameter $\theta = 1$ such ...
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Better prediction models with polling data?

I've been working on a project on measuring polls' accuracy in complex contexts (more than two candidates) where there are a small number of inaccurate polling data points. I thought it would be the ...
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Distribution of number of values less than cutoff within symmetric Dirichlet

Assume have a symmetric Dirichlet distribution with $a_1= \dots =a_k = a$ $ (X_1, \ldots, X_K)\sim\operatorname{Dir}(a) $ I am trying to determine the distribution of the number of values less than ...
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Distribution over a matrix of probabilities

I am interested in a problem where I need to infer the distribution of a matrix of probabilities, $\matrix{\Theta}$, where the rows and columns must sum to 1 and every entry lie in the range 0 and 1. ...
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80 views

Weighted sum of Dirichlets is Dirichlet

I am studying Sethuraman's paper on the Dirichlet process and having difficulty showing a lemma. He states: Let $\boldsymbol\gamma=(\gamma_1,...\gamma_k)$ and $\gamma=\sum_j \gamma_j$ and let ...
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What is an assignment matrix?

I'm trying to implement a topic model using a Latent Dirichlet allocation (LDA) algorithm. I'm using sentences as my dataset. What is Ck in the given instructions? The instructions are as follows: ...
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Unkown 6-sided dice. After 600 rolls frequency for all sides exactly equal. What is the chance, that rolling “6” with this dice has frequency > 1/6?

Although it is unknown dice, the symmetry of the evidence tells us, that we can treat the dice as fair, so the chance should be exactly 50%. But if we simulate it by hand, the result is less then ...
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difference between hierarchical dirichlet process and nested dirichlet process

There have some extensions to Dirichlet process. One is Hierarchical Dirichlet process, and another is Nested Dirichlet Process. What are the differences between these two? I once read the paper of ...
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253 views

understanding of effect of $\alpha$ in Dirichlet distribution

When reading the topic modeling tutorial written by Blei, KDD 2011 tutorial I was confused about a set of diagrams which aim to show the effect of $\alpha$ in Dirichlet distribution. For example, for ...
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simulate dirichlet process in R

I am reading the paper of "Dirichlet Process Mixtures of Generalized Linear Models" authored by L. A. Hannah. If I would like to simulate the following model $$\mathcal{P}\sim ...
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stick breaking model of Dirichlet process

I have a question regarding sticking-breaking model of Dirichlet process, which is defined as follows: There are further statements that I am not clear that how to derive equation 1 from that ...
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multivariate distributions bounded on [0,1] where parameters can be solved for from known mode

I need some kind of multivariate distribution which has the following properties support is $x_1,$ $x_2$, ..., $x_K$ where all $x_i \in [0,1]$ Though not required it is true that elements of the ...
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What to do for Dirichlet distribution when elements of X vector may be zero

So I want to define a Dirichlet distribution over frequency vectors which are unit vectors whose elements represent the frequency with which different characters occur in a body of text. Trouble is ...
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Can Dirichlet and multinomial distributions be defined from their univariate distributions this way?

For Dirichlet distribution: $X := [x_1, \cdots, x_K] \in [0,1]^K$, $x_i \sim {\rm beta}(\alpha_i, \beta_i)$ and $\sum x_i = 1$. Can we say the distribution of $X$ is a Dirichlet distribution? If ...