The Dirichlet-tree distribution
نویسنده
چکیده
This note further explores the Dirichlet-tree distribution developed by Dennis (1991). An inclusion relationship is given for different tree structures and an independence relationship is given for probabilities in the tree. The posterior, evidence, and predictive density are derived for multinomial observations.
منابع مشابه
Introducing of Dirichlet process prior in the Nonparametric Bayesian models frame work
Statistical models are utilized to learn about the mechanism that the data are generating from it. Often it is assumed that the random variables y_i,i=1,…,n ,are samples from the probability distribution F which is belong to a parametric distributions class. However, in practice, a parametric model may be inappropriate to describe the data. In this settings, the parametric assumption could be r...
متن کاملNon-Parametric Bayesian Sum-Product Networks
We define two non-parametric models for Sum-Product Networks (SPNs) (Poon & Domingos, 2011). The first is a tree structure of Dirichlet Processes; the second is a dag of hierarchical Dirichlet Processes. These generative models for data implicitly define a prior distribution on SPN of tree and of dag structure. They allow MCMC fitting of data to SPN models, and the learning of SPN structure fro...
متن کاملEfficient Tree-Based Topic Modeling
Topic modeling with a tree-based prior has been used for a variety of applications because it can encode correlations between words that traditional topic modeling cannot. However, its expressive power comes at the cost of more complicated inference. We extend the SPARSELDA (Yao et al., 2009) inference scheme for latent Dirichlet allocation (LDA) to tree-based topic models. This sampling scheme...
متن کاملSubtree prune and regraft: a reversible real tree-valued Markov process
We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and re-graft (SPR)Markov chains that appear in phylogenetic analysis. A key technical ingredient in this work is the use of a novel Gromov– Hausdorff type distance to metrize the space whose ...
متن کاملRobustness of compound Dirichlet priors for Bayesian inference of branch lengths.
We modified the phylogenetic program MrBayes 3.1.2 to incorporate the compound Dirichlet priors for branch lengths proposed recently by Rannala, Zhu, and Yang (2012. Tail paradox, partial identifiability and influential priors in Bayesian branch length inference. Mol. Biol. Evol. 29:325-335.) as a solution to the problem of branch-length overestimation in Bayesian phylogenetic inference. The co...
متن کامل