An nle() fit gives an unnormalized posterior,
\(q_\phi(x \mid \theta)\,p(\theta)\), but no way to draw from it directly.
neuralsbi samples it with a univariate slice sampler (Neal, 2003) run over
many chains at once.
Details
Slice sampling is the default in Python sbi for the same reason it is the
default here: it has no step size to tune, adapts its scale to the target as
it goes, and handles bounded supports without any special casing, because a
prior that returns -Inf outside its support simply shrinks the slice
interval.
The vectorization runs across chains rather than across dimensions. Every
chain proposes its next value for the same coordinate at the same time, so
one step costs one batched call to the density estimator instead of
n_chains separate forward passes. With a neural likelihood that difference
is the whole running time.
References
Neal, R. M. (2003). Slice sampling. The Annals of Statistics 31(3), 705-767. doi:10.1214/aos/1056562461
See also
posterior.nsbi_nle() for the arguments that control it, and
stan_code() for handing the same likelihood to NUTS instead.