Posterior from a neural likelihood — posterior.nsbi

Bayes' rule turns an nle() fit into a posterior, \(p(\theta \mid x) \propto q_\phi(x \mid \theta)\,p(\theta)\), but the result has no closed form and no direct sampler. posterior() on an nsbi_nle therefore returns an object that samples with MCMC, and sample() on it runs a chain rather than a forward pass.

Usage

# S3 method for class 'nsbi_nle'
posterior(
  fit,
  x_obs = NULL,
  sampler = c("slice", "stan"),
  n_chains = NULL,
  warmup = 200L,
  thin = 2L,
  init_strategy = c("resample", "proposal"),
  seed = NULL,
  max_batch = 1e+05,
  ...
)

Arguments

fit: An nsbi_nle object from nle().
x_obs: Observation to condition on. Rows are treated as independent observations from the same parameter, and the log-likelihood sums over them.
sampler: "slice" (the default) or "stan".
n_chains: Number of chains. The default depends on the sampler: 20 for "slice", which evaluates every chain in one batched call per step and so pays almost nothing for more of them, and 4 for "stan", where each chain is a separate process with its own warmup to pay for.
warmup: Steps discarded at the start of each chain.
thin: Keep one draw in thin. The default is 2: the slice width is adapted during warmup, and with that the retained draws are already close to independent – on a Gaussian target with 20 chains, thin = 2 gives a bulk ESS of about 96% of them. Since each evaluation is a forward pass over every observation, thinning harder buys very little for what it costs. Raise it if the reported ESS says you need to. (Python sbi thins by 1 by default; it thinned by 10 up to v0.21.)
init_strategy: "resample" (default, and sbi's) weights a pool of prior draws by the posterior density and resamples the starting points from it, drawing more pools as needed if the first one lands fewer than n_chains draws in the posterior's support; "proposal" skips the weighting and keeps whichever prior draws land inside the posterior's support, also drawing more pools as needed. "proposal" is cheaper per accepted draw, but every draw the posterior excludes is wasted: if only a fraction a of the prior's mass survives, roughly 1 / a draws are needed per starting point, so a posterior that rules out most of the prior can make "proposal" far slower than "resample" to find enough starting points, and it errors out once its draw budget is spent. The pool is 1000 draws, set with n_pool. sbi uses 10,000 per chain, which on a surrogate summed over thousands of observations is a large bill before the first MCMC step.
seed: Optional integer seed.
max_batch: Largest number of (theta, x) pairs evaluated in one call to the estimator, both at every MCMC step and in log_prob(). Only affects memory and speed; see max_batch on log_lik() for the same knob on a direct likelihood evaluation.
...: Further arguments to the sampler: width, max_steps and n_pool for "slice", or iter_warmup, iter_sampling and refresh for "stan".

Value

An object of class c("nsbi_nle_posterior", "nsbi_mcmc_posterior", "nsbi_posterior").

Details

Two samplers are available. "slice" is the default: a vectorized univariate slice sampler (see nsbi_mcmc) with nothing to tune and no dependencies. "stan" writes the fitted likelihood out as a Stan program (see stan_code()) and runs NUTS on it through cmdstanr or rstan, which mixes better on correlated posteriors at the cost of a one-time model compile.

Examples

prior <- prior_uniform(c(mu = -3), c(mu = 3))
fit <- nle(prior, function(mu) c(y = rnorm(1, mu, 0.5)),
           n_simulations = 1000, density_estimator = "linear_gaussian")

x_obs <- matrix(rnorm(50, mean = 1, sd = 0.5), ncol = 1)
post <- posterior(fit, x_obs, n_chains = 4, warmup = 50, thin = 2)
draws <- sample(post, 400)
colMeans(draws)
#>       mu 
#> 1.094471