Dependent mixtures of Dirichlet processes

An approach to modeling dependent nonparametric random density functions is presented. This is based on the well known mixture of Dirichlet process model. The idea is to use a technique for constructing dependent random variables, first used for dependent gamma random variables. While the methodology works for an arbitrary number of dependent random densities, with each pair having their own dependent structure, the mathematics and estimation algorithm is focused on two dependent random density functions. Simulations and a real data example are presented.

[1]  Spyridon J. Hatjispyros,et al.  A random dynamical system model of a stylized equity market , 2005 .

[2]  D. Dunson.  Bayesian dynamic modeling of latent trait distributions. , 2006, Biostatistics.

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

[4]  Michael C. Mackey,et al.  Chaos, Fractals, and Noise , 1994 .

[5]  J. E. Griffin,et al.  Order-Based Dependent Dirichlet Processes , 2006 .

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

[7]  D. Dunson,et al.  Kernel stick-breaking processes. , 2008, Biometrika.

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

[9]  J. Craggs.  Applied Mathematical Sciences , 1973 .

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

[11]  N. Pillai,et al.  Bayesian density regression , 2007 .

[12]  Stephen G. Walker,et al.  A Bayesian nonparametric estimator of a multivariate survival function , 2009 .

[13]  Stephen G. Walker,et al.  A Bayesian nonparametric study of a dynamic nonlinear model , 2009, Comput. Stat. Data Anal..

[14]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[15]  P. Müller,et al.  A method for combining inference across related nonparametric Bayesian models , 2004 .

[16]  Stephen G. Walker,et al.  Slice sampling mixture models , 2011, Stat. Comput..

[17]  Spyridon J. Hatjispyros,et al.  Parameter estimation for random dynamical systems using slice sampling , 2007 .