Bayesian two-sample tests

In this paper, we present two classes of Bayesian approaches to the two-sample problem. Our first class of methods extends the Bayesian t-test to include all parametric models in the exponential family and their conjugate priors. Our second class of methods uses Dirichlet process mixtures (DPM) of such conjugate-exponential distributions as flexible nonparametric priors over the unknown distributions.

[1]  H. Hotelling.  A Generalized T Test and Measure of Multivariate Dispersion , 1951 .

[2]  P. Bickel.  A Distribution Free Version of the Smirnov Two Sample Test in the $p$-Variate Case , 1969 .

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

[4]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[5]  J. Friedman,et al.  Multivariate generalizations of the Wald--Wolfowitz and Smirnov two-sample tests , 1979 .

[6]  N. H. Anderson,et al.  Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates , 1994 .

[7]  N. Henze,et al.  On the multivariate runs test , 1999 .

[8]  Pierre Baldi,et al.  A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes , 2001, Bioinform..

[9]  J. Berger,et al.  Bayesian and Conditional Frequentist Testing of a Parametric Model Versus Nonparametric Alternatives , 2001 .

[10]  P. Hall,et al.  Permutation tests for equality of distributions in high‐dimensional settings , 2002 .

[11]  László Györfi,et al.  On the asymptotic properties of a nonparametric L/sub 1/-test statistic of homogeneity , 2005, IEEE Transactions on Information Theory.

[12]  Richard J. Fox,et al.  A two-sample Bayesian t-test for microarray data , 2006, BMC Bioinformatics.

[13]  Katherine A. Heller,et al.  Bayesian hierarchical clustering , 2005, ICML.

[14]  Bernhard Schölkopf,et al.  A Kernel Method for the Two-Sample-Problem , 2006, NIPS.

[15]  Hans-Peter Kriegel,et al.  Integrating structured biological data by Kernel Maximum Mean Discrepancy , 2006, ISMB.

[16]  Bernhard Schölkopf,et al.  Correcting Sample Selection Bias by Unlabeled Data , 2006, NIPS.

[17]  Max Welling,et al.  Accelerated Variational Dirichlet Process Mixtures , 2006, NIPS.

[18]  Michael I. Jordan,et al.  Variational inference for Dirichlet process mixtures , 2006 .

[19]  Yee Whye Teh,et al.  Collapsed Variational Dirichlet Process Mixture Models , 2007, IJCAI.

[20]  Arthur Gretton,et al.  Nonparametric Independence Tests: Space Partitioning and Kernel Approaches , 2008, ALT.