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

[Murray Jorgensen]

Rolf, I didn't ask any question about the EM algorithm, or about MML for 
that matter, I was just indicating the context in which my query first 
arose. To avoid any tangents to my tangent and to suppress any fuzziness 
which Rolf and I both deplore I will repeat the question:

_Are their any Bayesians who attempt to make a distinction between 
parameters and unobserved random variables and if so, how and why?_

(Possibly the wrong group to address such a question to, though I could 
attempt to defend my choice of group if required!)

Murray

Rolf Turner wrote:
> 
> 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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-- 
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