[SciPy-User] OT: The standard of Bayesian statistics textbooks (rant)
Andrew Jaffe
a.h.jaffe at gmail.com
Sun Jun 15 03:23:28 EDT 2014
Hi,
On 15/06/2014 01:26, Sturla Molden wrote:
> Nathaniel Smith <njs at pobox.com> wrote:
>
>> Of course any integral can be written as an expectation, but if you have a
>> tractable general method for computing the expected value of arbitrary
>> distributions then you should publish it and collect your Fields medal.
>
> In this particular case (pseudocode):
>
> for i in range(n):
> theta[i] ~ p(theta | M), e.g. by Markov Chain Monte Carlo
> L[i] = p(y | theta[i] )
> p(y | M) = mean( L[burnin:] )
>
> Can I have my Fields medal now?
This is relatively well known (at least in my field, cosmology) as the
"Blackwell-Rao" estimate of the model likelihood (aka model likelihood
aka Bayesian evidence). Unfortunately in very many cases it has very bad
properties, especially in the tails.
Moreover, one of the advantages of the sampling methods is that it is
often easier to sample from the likelihood than to actually compute it.
Yours,
Andrew
>
> ;-)
>
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