model selection via Bayes factors in Turing.jl

[SimonEnsemble]

interested in model selection via Bayes factors.

my understanding is that Turing.jl currently provides no functionality for this.

this blog post shows how we can numerically integrate the posterior with quadrature to obtain the evidence, provided (i) there aren't too many params to make this integral high-dimensional and (ii) we can evaluate the posterior at a given value of the params.

what do you think of the following approach to computing Bayes' factors, using Turing.jl (my models only have 2-3 params 😄).

• sample to obtain a chain as in the tutorials of Turing.jl.
• use kernel density estimation method to approximate the posterior distribution over param space
• feed kernel density estimate into a numerical quadrature routine to compute evidence.

[SimonEnsemble]

if this approach makes sense, happy to write a short tutorial demonstrating this, for Turing.jl.

[gretarsson]

Did you make the tutorial?

[SimonEnsemble]

no---no one responded so I assumed no interest. 😭
could do on a 'rainy day' this summer if this would be of interest, though!

[torfjelde]

Completely missed this 😬 But indeed seems interesting! Think we'd be very happy to have a tutorial like this

@yebai