[SciPy-User] OT: The standard of Bayesian statistics textbooks (rant)

[Andrew Jaffe]

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



>
> ;-)
>