[SciPy-User] [OT] Bayesian vs. frequentist

Charles R Harris charlesr.harris@gmail....
Tue Feb 14 22:15:04 CST 2012


On Tue, Feb 14, 2012 at 8:49 PM, Travis Oliphant <travis@continuum.io>wrote:

>
> > Coincidentally, this discussion:
>> >
>> http://andrewgelman.com/2012/02/adding-an-error-model-to-a-deterministic-model/
>> > started when a civil engineering PhD posted a request for help.  My
>> reading
>> > of the ensuing discussion of both posts is that there is still a lot of
>> > work to
>> > do in bridging statistics (bayesian or frequentist) and deterministic
>> > modeling
>> > of complex systems.
>>
>> I don't quite see why there should be anything deterministic (in the
>> sense of correctly described by a mathematical model) about the growth
>> of bacteria and the response of living tissue, (as there is nothing
>> deterministic in the behavior of the macro economy). In economics we
>> just add a noise variable (unexplained environmental or behavioral
>> shocks) everywhere.
>>
>> I thought these were exactly the kind of dynamic problems that Kalman
>> Filter (or it's nonlinear successors) were invented for.
>>
>> My main impression of the two articles and discussion is that being a
>> Bayesian is a lot of work if you need to have a fully specified prior
>> and likelihood, instead of just working with some semi-parametric
>> estimation method (like least squares) that still produces results
>> even if you don't have a fully specified likelihood. (It might not be
>> efficient compared to the case when you have full information, but
>> your results are less wrong than if your full specification is wrong.)
>>
>>
> Well, invented priors can be used to bias parametric results for political
> purposes. Thar's gold in them priors. So there is that ;)
>
> I read E. T. Jaynes early papers and his book and enjoyed them, but I
> think treating physical entropy by Bayesian methods was a bit much. I don't
> think think the thermodynamic properties of a system depend on the
> observers knowlege. I would say both methods have their place, just use the
> right one for the problem at hand.
>
>
> It sounds like we will have to revisit your views there over drinks
> sometime.     I think the whole point is that there is really no such thing
> as physical entropy.   It's all just a property that you have to assign to
> a system if you want maximum reproducibility without constraining
> everything.   That's the way I prefer to think about it at this point
> anyway ;-)
>
>
Classically, it's an assumption about the behavior of the dynamical
systems. It doesn't even need to be exactly so. But in any case, it is a
dynamical problem, not a knowledge problem, and has physical affects that
have nothing to do with the observer. Heat flows from hot to cold whatever
you care to think. A watched pot on the stove *does* boil. Where things get
interesting is if you start manipulating the system, start measuring things
or put in a Maxwell's demon. Then there is an interplay. Deeper down, one
might start asking questions about the physical representation of the
knowledge in the observer.

Chuck

>
>
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