[R-sig-ME] Parameters and unobserved random variables - was Re: lmer: ML and REML estimation

[Murray Jorgensen]

Perhaps a bit of a tangent so I have adjusted the subject line. About 10 
years ago I was visiting the late Professor Chris Wallace at Monash and 
getting into discussions about the relationship between the EM algorithm 
and his "minimum message length" approach to inference. Chris was 
adamant it treating what I thought of as "unobserved random variables" 
as "parameters". Now Chris was a Bayesian and so for him all parameters 
were random variables. It would seem that if you are a Bayesian that no 
consistent distinction can be made between parameters and unobserved 
random variables. Are their any Bayesians who attempt to make such a 
distinction and if so, how and why?

Murray

Douglas Bates wrote:
[...]
> I read the phrase "some of the parameters are random variables" to be
> referring to the random effects.  I phrase things slightly
> differently.  In particular I don't regard the random effects as
> parameters. I regard a mixed-effects model as being based on two
> random variables: the response Y whose value, y, has been observed and
> an unobserved random effects vector B.  
[...]
-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441   Mobile 021 0200 8350