"resample" (the default, and sbi's) draws a large pool from the prior,
weights it by the posterior density and resamples without replacement: a
sampling-importance-resampling start that puts the chains where the mass is,
which matters because slice sampling has no adaptation phase to rescue a bad
start. If one pool does not contain n_chains finite draws, more are drawn
and pooled in – see mcmc_init_resample(). "proposal" just takes prior
draws, keeping whichever land inside the posterior's support, which is
cheaper per draw but wastes every draw the posterior excludes – see
mcmc_init_proposal().
Usage
mcmc_init(
prior,
log_prob_fn,
n_chains,
strategy = c("resample", "proposal"),
n_pool = 1000L
)Details
Two departures from sbi, both about the case this exists for. sbi draws
its pool once per chain, so 20 chains cost 20 pools; one pool shared across
chains costs a twentieth of that and, drawn without replacement, gives
distinct starting points rather than independent ones that may coincide. And
the weighting stays in log space: sbi normalizes the log weights and
exponentiates, which is fine until a few thousand independent observations
spread the log-likelihood over prior draws by thousands of nats and every
weight but a handful underflows to zero.