Bayesian Selection of Decomposable Models With Incomplete Data

This article describes a new approach to Bayesian selection of decomposable models with incomplete data. This approach requires the characterization of new ignorability conditions for the missing-data mechanism and the development of new computational methods. Both issues are considered, and solutions are proposed. Theory and methods are assessed in controlled experiments and in the analysis of one real-life incomplete dataset.

[1]  Paola Sebastiani,et al.  Bayesian Inference with Missing Data Using Bound and Collapse , 2000 .

[2]  David E. Booth,et al.  Analysis of Incomplete Multivariate Data , 2000, Technometrics.

[3]  Wasserman,et al.  Bayesian Model Selection and Model Averaging. , 2000, Journal of mathematical psychology.

[4]  Michael I. Jordan.  Graphical Models , 2003 .

[5]  L. Wasserman,et al.  Computing Bayes Factors by Combining Simulation and Asymptotic Approximations , 1997 .

[6]  D. Heitjan,et al.  Distinguishing “Missing at Random” and “Missing Completely at Random” , 1996 .

[7]  D. Rubin.  Multiple Imputation After 18+ Years , 1996 .

[8]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[9]  Daniel F. Heitjan,et al.  Ignorability in general incomplete-data models , 1994 .

[10]  Taesung Park,et al.  Models for Categorical Data with Nonignorable Nonresponse , 1994 .

[11]  A. Dawid,et al.  Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models , 1993 .

[12]  D. Rubin,et al.  Ignorability and Coarse Data , 1991 .

[13]  Andrew L. Rukhin,et al.  Tools for statistical inference , 1991 .

[14]  D. Rubin,et al.  Multiple imputation for nonresponse in surveys (book review) , 1989 .

[15]  Nan M. Laird,et al.  Regression Analysis for Categorical Variables with Outcome Subject to Nonignorable Nonresponse , 1988 .

[16]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[17]  C. N. Morris,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[18]  A. Dawid.  Conditional Independence for Statistical Operations , 1980 .

[19]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[20]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[21]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[22]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[23]  Irving John Good,et al.  The Estimation of Probabilities: An Essay on Modern Bayesian Methods , 1965 .