Generalise the prior input to NonParametric() beyond Dirichlet

[seabbs-bot]

Summary

Currently NonParametric() accepts either a numeric PMF (fixed) or a Dirichlet() prior (estimated, via the gamma‑normalisation trick on the simplex). It would be worth thinking about whether the prior input should be generalised so that other distributions over a simplex can be plugged in.

Motivation

The Dirichlet works well as a default — one concentration knob, easy structural‑zero handling, simple ragged Stan implementation. But for some use cases other priors would be more appropriate:

• Smoothness across bins: neighbouring delay bins are usually similar in mass. A random walk / AR(1) on the log‑PMF (i.e. softmax of an MVN with structured covariance) would express that, while a Dirichlet treats bins as exchangeable.
• Correlated uncertainty: if you have prior covariance information (e.g. from a previous fit summarised as posterior draws), a MVN on logits captures it; Dirichlet only has the fixed mildly‑negative covariance implied by α.
• Posterior re‑use: if get_parameters(fit) ends up returning a posterior summary as a dist_spec, having more than one option keeps the round‑trip honest when the moment‑matched Dirichlet would be a poor fit.

Concretely, future options to consider:

• A LogitNormal() / SoftmaxMVN() dist_spec that NonParametric(pmf = ...) could accept.
• A dedicated SmoothNonParametric() / RWPmf() constructor with a smoothing prior on the log‑PMF (probably the more user‑friendly framing).

Out of scope

Not blocking the current Dirichlet PR (#1338). This is a design question for after that lands.

This was opened by a bot. Please ping @seabbs for any questions.

[seabbs]

This could borrow from the work going into non parametric estimation in primarycensored and by borrow i mean vendor the code.