"resample" starting points: pool prior draws, then SIR without replacement

A single pool of max(n_pool, n_chains) prior draws can land fewer than n_chains of them in the posterior's support – the same shape of problem mcmc_init_proposal() fixed for "proposal". Padding the shortfall by recycling (rep_len() on too few indices) used to start several chains from identical points, which defeats the diagnostics downstream: split-Rhat and bulk ESS both assume the chains they compare started from distinct locations, and a repeated start makes chains look more agreed than they are.

Usage

mcmc_init_resample(prior, log_prob_fn, n_chains, n_pool = 1000L)

Details

Instead, more pools are drawn and their finite draws accumulated until n_chains distinct ones are collected (up to 20 attempts, the same budget mcmc_init_proposal() uses), and the final start is a weighted resample without replacement from that accumulated, still-distinct set – not from a single pool. If the budget runs out first, the error distinguishes a genuinely degenerate surrogate (no draw at all landed in support) from a merely low acceptance rate (some did, just not n_chains of them).