Visualization of Conjugate Distributions in Latent Dirichlet Allocation Model

In Bayesian probability theory, if the posterior distributions p(θ|x) are in the same family as the prior probability distribution p(θ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function. In the Latent Dirichlet Allocation model, the likelihood function is Multinomial and the prior function is Dirichlet. There the Dirichlet distribution is a conjugate prior and then the posterior function becomes also Dirichlet. The posterior function is a parameter mixture distribution where the parameter of the likelihood function is distributed according to the given Dirichlet distribution. The compound probability distribution is, however, complicated to understand and have the image. To make many persons understand the image intuitively, the paper visualizes the parameter mixture distribution.