Probabilistic measures with Monte Carlo draws

Sometimes we don't have a density function for a predictive distribution but instead have IID draws from that distribution. e.g. in Bayesian inference, we often only have access to the posterior predictive distribution through Monte Carlo draws. It would be useful if this package supported statistical estimation of the measure in such cases.

Proposal

I propose the API for probabilistic measures be expanded so that the first argument to a probabilistic measure can be an array of predictions representing these draws instead of just a distribution, where possible (e.g. this would not be possible for LogScore). When the first argument is an array of draws, then weights must be an array with the same size.

Example: CRPS

For example, the continuously ranked probability score (CRPS) can be defined for a predictive distribution q as
CRPS(q, y) = E[|ŷ-y|] - E[|ŷ-ŷ'|], where ŷ' and ŷ are independent random variables drawn from q.
For many named distributions, this can be evaluated exactly. But it can also be estimated from draws.

The naive estimator of CRPS for an IID sample of size N is.
mean(abs.(ŷ .- y)) - mean(abs.(ŷ .- ŷ')) * (N // (2 * (N-1))). For continuous predictions, this can be reformulated using order statistics to reduce the cost to O(Nlog(N)) (see https://hal.science/hal-02976423/document)

Start by reading the existing probabilistic-measure entry points and the CRPS implementation, then compare them with the proposal's array-of-draws API and weighting requirements. Done means supported measures accept draw arrays with same-sized weights where possible, while unsupported cases such as LogScore remain defined.