Posterior from a neural ratio

Bayes' rule turns an nre() fit into a posterior, \(p(\theta \mid x) \propto r_\phi(\theta, x)\,p(\theta)\), and as with nle() the result has no closed form and no direct sampler. posterior() on an nsbi_nre 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_nre'
posterior(
  fit,
  x_obs = NULL,
  n_chains = 20L,
  warmup = 200L,
  thin = 2L,
  init_strategy = c("resample", "proposal"),
  seed = NULL,
  max_batch = 1e+05,
  ...
)

Arguments

fit

An nsbi_nre object from nre().

x_obs

Observation to condition on. Rows are treated as independent observations from the same parameter, and the log ratio sums over them.

n_chains

Number of chains. The slice sampler evaluates every chain in one batched call per step, so more chains cost almost nothing.

warmup

Steps discarded at the start of each chain.

thin

Keep one draw in thin. See posterior.nsbi_nle() for why the default is 2.

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.

seed

Optional integer seed.

max_batch

Largest number of (theta, x) pairs evaluated in one call to the classifier, both at every MCMC step and in log_prob(). Only affects memory and speed; see max_batch on log_ratio() for the same knob on a direct ratio evaluation, and matters most here since the ratio classifier has no i.i.d. fast path – every pair costs a forward pass.

...

Further arguments to the sampler: width, max_steps and n_pool.

Value

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

Details

There is one sampler here, the vectorized slice sampler of nsbi_mcmc, and no sampler argument to choose it with. nle()'s "stan" option works by transpiling the fitted density into a Stan functions block; the residual classifier behind a ratio estimator has no such export, so NUTS is not on offer.

Examples

prior <- prior_uniform(c(mu = -3), c(mu = 3))
fit <- nre(prior, function(mu) c(y = rnorm(1, mu, 0.5)),
           n_simulations = 1000, classifier = "logistic")

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 
#> 1.024003