Samplers for discrete (nominal) spaces

[pglpm]

R/Fortran, Linux, x86_x64

(Following this issue comment)

I see that Paramonte offers sampling on continuous, Rⁿ spaces. I'd like to request some sampling capability on finite, discrete spaces, and Cartesian products of real and discrete spaces. This kind of sampling is very important for nominal data.

Ordinal data can be sampled by a continuous sampler by introducing a continuous latent variate, and then considering the ordinal variate as an indicator-function over the continuous-variate's space. This also takes care of some degree of smoothing (reflecting an a-priori low expectation of many big jumps) of the probability distribution for the ordinal variate.

But this very smoothing effect is why this kind of latent-variate approach does not work well with nominal data, whose values can in principle be arbitrarily shuffled.

Data of this type occur very frequently in medical applications. Typical medical predictors include nominal data such as presence/absence of particular genes (binary variates, including sex), membership in one or another risk groups that don't have any specific ordering, and similar variates. Often the predictors also include interval and ordinal variates (volumes of internal organs, blood levels, age, Likert scales, and similar). See the example in this preprint.

I am trying to develop an R package for Bayesian nonparametric density inference, especially for use in medicine, that is enough flexible to include all these kinds of variates, and at the same time is as user-friendly as possible, not requiring the clinician to worry about Monte Carlo sampling. Paramonte would be wonderful for this. At the moment my prototype package uses Nimble for Monte Carlo sampling. Nimble offers built-in categorical and Dirichlet/simplex samplers that can be combined with samplers for continuous spaces.

Thank you for this great project!

[shahmoradi]

Thank you @pglpm, for the issue and the examples! This is a great starting point for the devs.