Monte-Carlo Hellinger distance between a fit and its target

Estimates the squared Hellinger distance H^2(f, g) = 1 - integral sqrt(f(x) g(x)) dx by importance sampling against the proposal stored in the fit (for regime "kld") or by sampling from the fit itself (for regime "sample"). The target's log_density must be supplied and normalised; otherwise the Monte Carlo integral is biased by the missing \(\sqrt{Z(f)}\). When the target's normalised property is not TRUE, a warning is issued and the returned value is flagged.

Usage

hellinger_mc(fit, n_mc = 5000L, seed = NULL)

Arguments

fit

A gmm_fit whose target carries a log_density.

n_mc

Number of Monte Carlo samples.

seed

Optional integer seed.

Value

A list with components

• h2 - estimate of H^2(f, g),

• se - Monte Carlo standard error,

• n_mc - sample size used.

See also

Other diagnostics: bic_aic(), ess_summary(), ess_trace(), gmm_anneal_path(), gmm_conditional_entropy(), gmm_entropy(), gmm_evidence(), gmm_fit_ensemble(), gmm_fit_quality(), gmm_independence_graph(), gmm_mutual_information(), kld_trace(), proxy_functional_ci()

Examples

fit <- fit_proxymix(banana_target(), N = 3L, regime = "kld",
                    is_size = 2000L, max_iter = 25L, seed = 1L)
hellinger_mc(fit, n_mc = 1000L, seed = 1L)
#> $h2
#> [1] -0.01135163
#> 
#> $se
#> [1] 0.005185913
#> 
#> $n_mc
#> [1] 2000
#> 
#> $trustworthy
#> [1] TRUE
#>