Evaluate a learned likelihood-to-evidence ratio

log_ratio() evaluates the ratio learned by nre(), \(\log r(\theta, x) = \log p(x \mid \theta) - \log p(x)\).

Usage

log_ratio(fit, theta, x, ...)

# S3 method for class 'nsbi_nre'
log_ratio(fit, theta, x, sum_iid = TRUE, max_batch = 1e+05, ...)

Arguments

fit

An nsbi_nre fit from nre().

theta

Parameter values: a numeric vector (one parameter set) or an n_theta x dim_theta matrix.

x

Observed data: a numeric vector (one observation) or an n_obs x dim_x matrix whose rows are independent observations.

...

Unused, for S3 consistency.

sum_iid

Sum the log ratio over the rows of x (the default). Set FALSE to get the per-observation values instead.

max_batch

Largest number of (theta, x) pairs evaluated in one call to the classifier. Only affects memory and speed.

Value

With sum_iid = TRUE, a numeric vector with one entry per row of theta. With sum_iid = FALSE, an n_theta x n_obs matrix.

Details

Rows of x are treated as independent observations from the same parameter, so by default the result sums over them. That sum is the log-likelihood of the whole data set up to an additive constant that does not depend on theta, which is all a posterior needs and all NRE learns: the evidence term \(\log p(x)\) is never estimated separately, so log_ratio() is not a log-likelihood you can compare across observations. Differences between two theta at the same x are exactly the differences in log-likelihood.

See also

posterior() to turn the ratio into posterior draws, log_lik() for the nle() equivalent that is a calibrated log-likelihood.

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(20, mean = 1, sd = 0.5), ncol = 1)
grid <- matrix(seq(-2, 2, length.out = 5), ncol = 1)
log_ratio(fit, grid, x_obs)
#> [1] -370.224203 -141.967041    3.034027   64.779000   43.267879