Options for sampling discrete parameters?

[erccarls]

Any chance this could be added? Is this even a possibility for the Multinest Algorithm in general?

[andrewfowlie]

Your could implement this yourself in your prior function. You must map the MultiNest unit hypercube to your parameter space. To map to a discrete parameter p taking values from 1 ... n from a MultiNest parameter from a unit hypercube, i.e. x \sim U(0,1), consider the following pseudo-code:

for i in 1 ... n:
    if x < i / n:
        p = i
        return p

i.e. divide 0 to 1 into n equal intervals and map each interval to a value of p. This could be generalized any discrete parameter y_p indexed by p, where all values of p are equally probable.

I see no problems with mapping from a continuous to a discrete parameter space, as you can always rewrite the evidence, Z, in terms of a continuous parameter. That is, instead of a discrete sum over i

Z = \sum_i like(i) prior(i)

you could write an integral with a continuous parameter x

Z = \int like(x) prior(x) dx = \sum_i like(i) prior(i)

where prior(x) and like(x) are constant for values of the continuous parameter x that correspond to the discrete parameter i. A small caveat: I don't know whether MultiNest would be the quickest algorithm to perform a sum for an evidence (rather than an integral for an evidence).

[rjw57]

Hi @innisfree and @erccarls

[rjw57]

Thanks for your interest in MultiNest but this is just a personal fork of the project. The project's home page is https://ccpforge.cse.rl.ac.uk/gf/project/multinest/ and there should be contact info there.

[andrewfowlie]

@rjw57 sure no worries. I just realized I could answer the question pretty easily so why not