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

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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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18 views

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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43 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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58 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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30 views

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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83 views

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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52 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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19 views

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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55 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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47 views

What is the intuition behind Dirichlet distribution?

looking for explanation on similar lines What is the intuition behind beta distribution?
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42 views

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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16 views

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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54 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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131 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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18 views

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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39 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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108 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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90 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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47 views

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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59 views

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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31 views

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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39 views

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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76 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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22 views

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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150 views

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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193 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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381 views

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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32 views

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 ...
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136 views

Gibbs sampling with Dirichlet Likelihood

I have a sequence of observations that I am representing as proportions: X1 X2 X3 X4 X5 0.10 0.20 0.50 0.12 0.08 0.07 0.24 0.55 0.04 0.10 ... ...
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1answer
309 views

How to calculate model error (like MSE) for a multivariate proportional response?

I have data where the response is multivariate and proportional (rows [observations] sum to 1). I am modelling this response using a Dirichlet regression via the DirichletReg R package where the ...
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452 views

Why does nobody use the Bayesian multinomial Naive Bayes classifier?

So in (unsupervised) text modeling, Latent Dirichlet Allocation (LDA) is a Bayesian version of Probabilistic Latent Semantic Analysis (PLSA). Essentially, LDA = PLSA + Dirichlet prior over its ...
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Laplace smoothing and Dirichlet prior

On the wikipedia article of Laplace smoothing (or additive smoothing), it is said that from a Bayesian point of view, this corresponds to the expected value of the posterior distribution, using a ...
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193 views

Dirichlet process mixture model with Bayesian hierarchical clustering

I am doing Bayesian hierarchical clustering. From my understanding, there are three basic points for this algorithm. Use marginal likelihoods to decide which clusters to merge Asks what the ...
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1answer
115 views

How to draw samples from a Bayesian nonparamatric density estimation? [DPpackage]

I am trying to compute a Kernel Density from high dimensional data ($n > 2$). The underlying (generative) model is assumed unknown. The goal is to draw samples from this estimate, in a sense ...
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235 views

The meaning of representing the simplex as a triangle surface in Dirichlet distribution?

I'm reading from a book that introduces the Dirchilet distribution and then presented figures about it. But I was not really able to understand those figures. I attached the figure here at the bottom. ...
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170 views

What does it mean to sample a probability vector from a Dirichlet distribution?

I'm essentially learning about Latent Dirichlet Allocation. I'm watching a video here: http://videolectures.net/mlss09uk_blei_tm/ and stuck at minute 45 when he started to explain on sampling from the ...
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118 views

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 ...
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474 views

Gibbs sampling for LDA — does a small Dirichlet concentration parameter make a difference?

I'm using a Gibbs sampler for Latent Dirichlet allocation as described by Griffiths and Steyvers (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC387300/). The sampling of a new topic $j$ for word $i$ is ...