Bayesian Nonparametric Mixture Models Using NIMBLE

This paper describes and illustrates new features of the NIMBLE computing environment (de Valpine et al., 2017) that enable simulation-based inference for general nonparametric Bayesian mixture models.

[1]  Lancelot F. James,et al.  Approximate Dirichlet Process Computing in Finite Normal Mixtures , 2002 .

[2]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[3]  Alan E. Gelfand,et al.  A Computational Approach for Full Nonparametric Bayesian Inference Under Dirichlet Process Mixture Models , 2002 .

[4]  J. Pitman.  Some developments of the Blackwell-MacQueen urn scheme , 1996 .

[5]  Martyn Plummer,et al.  JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling , 2003 .

[6]  Andrew Gelman,et al.  R2WinBUGS: A Package for Running WinBUGS from R , 2005 .

[7]  Peter Müller,et al.  DPpackage: Bayesian Semi- and Nonparametric Modeling in R , 2011 .

[8]  Lancelot F. James,et al.  Gibbs Sampling Methods for Stick-Breaking Priors , 2001 .

[9]  Jiqiang Guo,et al.  Stan: A Probabilistic Programming Language. , 2017, Journal of statistical software.

[10]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[11]  Michael C. Hughes,et al.  bnpy : Reliable and scalable variational inference for Bayesian nonparametric models , 2014 .

[12]  D. Blackwell,et al.  Ferguson Distributions Via Polya Urn Schemes , 1973 .

[13]  J. Sethuraman.  A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS , 1991 .

[14]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[15]  J. Pitman.  Exchangeable and partially exchangeable random partitions , 1995 .

[16]  Radford M. Neal.  Markov Chain Sampling Methods for Dirichlet Process Mixture Models , 2000 .

[17]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[18]  Dustin Tran,et al.  Deep Probabilistic Programming , 2017, ICLR.

[19]  A. Canale.  msBP: An R Package to Perform Bayesian Nonparametric Inference Using Multiscale Bernstein Polynomials Mixtures , 2017 .

[20]  Michael,et al.  On a Class of Bayesian Nonparametric Estimates : I . Density Estimates , 2008 .

[21]  Andrew Thomas,et al.  The BUGS project: Evolution, critique and future directions , 2009, Statistics in medicine.

[22]  Alan Edelman,et al.  Julia: A Fast Dynamic Language for Technical Computing , 2012, ArXiv.

[23]  Kai Xu,et al.  Turing: Composable inference for probabilistic programming , 2018, International Conference on Artificial Intelligence and Statistics.

[24]  Guido van Rossum,et al.  Python Programming Language , 2007, USENIX Annual Technical Conference.

[25]  M. Escobar.  Estimating Normal Means with a Dirichlet Process Prior , 1994 .