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
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
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,
>
> I have a multiple imputation procedure created according to some Bayesian model,
>performing
>
> (1) random draws for the parameters theta from their observed-data posterior and
>
> (2) random draws for the missing values Ymis according to their conditional
>predictive distribution f(Ymis|Yobs, theta) given the observed data and an actual
>draw of theta from (1).
>
> As far as I have understood the concept of properness this procedure obviously is
>Bayesianly proper as defined by Schafer (1997) as well as it is proper in the sense
>of Rubin (1987) just by definition. Now I am no longer sure about the latter - can
>anybody give me a pointer?
>
> Many thanks
> Susanne
>
> -------------------------------------------------------------------
> Dr. Susanne R�ssler
> Institute of Statistics and Econometrics
> University of Erlangen-Nuernberg, Germany
> email: [EMAIL PROTECTED]
>
>
___________________________________________________________________________________
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
