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

[Rolf Turner]

On 30/03/2009, at 9:44 AM, Murray Jorgensen wrote:

> 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?

Point of order, mister chairman.  The EM algorithm is just that:  an
algorithm.  (Or rather, it is a technique for *constructing* algorithms,
but that's another story.)  It is a technique for maximizing the  
likelihood
of a model and set of data where a part of the data is missing.  So the
issue is the relationship between ``minimum message length'' and  
``maximum
likelihood in the presence of missing data''.  The EM algorithm is  
just one
approach to maximizing such a likelihood; there are (in some contexts  
at least)
others and it doesn't really matter which technique you use.  The  
model is
the same; the way you get a numerical fit to the model doesn't matter  
in any
fundamental way.

I know I'm being picky/pedantic/dogmatic and so on, but in  
discussions of topics
like this if any fuzziness is left lying around confusion can easily  
set in and
people can very easily wind up talking at cross-purposes.

Sorry for wasting band-width if this is all toadally obvious to  
everyone else.

	cheers,

		Rolf Turner



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