Susanne: you are right that this is Bayesianly proper. For it to be proper in Rubin's frequentist sense, some assumptions about validity of the model are required -- clearly imputations generated from an idiotic =20 Bayesian model will have poor frequency properties. For example in repeated-measures data with dropouts, "the predictive distribution of the missing values is centered at the last recorded value with zero variance" is a Bayesian model for the (too-much-loved) "last obervation carried forward" imputation; this method has terrible frequency properties if the model is wrong!)
Technicalities aside, any imputation method implies a model for the predictive distribution of the missing values. The important point is to model that as well as possible, and then propagate the=20 uncertainty. Whether you are Bayesian or not, MI is a useful tool for doing this. Rod Little On Thu, 9 Nov 2000, Susanne Raessler wrote: > Dear Imputers, >=20 > I have a multiple imputation procedure created according to some Bayesian= model, performing >=20 > (1) random draws for the parameters theta from their observed-data poster= ior and >=20 > (2) random draws for the missing values Ymis according to their condition= al predictive distribution f(Ymis|Yobs, theta) given the observed data and = an actual draw of theta from (1). >=20 > As far as I have understood the concept of properness this procedure obvi= ously is Bayesianly proper as defined by Schafer (1997) as well as it is pr= oper in the sense of Rubin (1987) just by definition. Now I am no longer su= re about the latter - can anybody give me a pointer? >=20 > Many thanks > Susanne >=20 > ------------------------------------------------------------------- > Dr. Susanne R=E4ssler > Institute of Statistics and Econometrics > University of Erlangen-Nuernberg, Germany > email: [email protected] >=20 >=20 ___________________________________________________________________________= ________ Roderick Little Chair, Department of Biostatistics (734) 936-1003 U-M School of Public Health Fax: (734) 763-2215 M4208 SPH II [email protected] 1420 Washington Hgts http://www.sph.umich.edu/~rlittle/ Ann Arbor, MI 48109-2029
