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Percentile interval for any functional of a fitted proxy

Source: R/ensemble.R
proxy_functional_ci.Rd

Applies a functional to every member of a bootstrap ensemble and returns the base fit's point estimate with percentile confidence limits. The functional may return a scalar or a fixed-length numeric vector – the moments (gmm_mean(), gmm_cov()), a tail probability via pgmm() on a marginal, an entropy, a conditional mean, or any composition of the operator calculus.

Usage

proxy_functional_ci(ensemble, fn, level = 0.9, ..., tail_warn = 0.001)

Arguments

ensemble

A gmm_ensemble from gmm_fit_ensemble().

fn

A function mapping a gmm to a numeric scalar or vector.

level

Confidence level. Default 0.9.

...

Forwarded to fn.

tail_warn

Threshold for the tail-probability warning described in Details. Default 1e-3; NULL or 0 turns the warning off.

Value

A data frame with one row per element of fn's value: term, estimate (the base fit's value), conf.low, conf.high.

Details

The interval measures how much the functional moves when the fit is repeated on re-weighted draws. It does not measure how far the Gaussian-mixture family itself is from the target, so it can exclude the target's true value when the mixture has too few components. The gap is widest far in a tail: a mixture of Gaussians has Gaussian tails and can misstate a small tail probability by orders of magnitude while the interval stays narrow. A warning of class proxymix_tail_functional is raised when every value of fn (at the base fit and at every member) lies in [0, 1] and some element of the base fit's estimate, or its complement, is below tail_warn. Check such a probability against numerical integration of the target or a method built for tails.

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(), hellinger_mc(), kld_trace()

Examples

fit <- fit_proxymix(banana_target(), N = 2L, regime = "kld",
                    is_size = 1500L, max_iter = 20L, seed = 1L)
ens <- gmm_fit_ensemble(fit, B = 30L, seed = 2L)
proxy_functional_ci(ens, function(g) gmm_mean(g)[1L])
#>   term     estimate    conf.low  conf.high
#> 1   f1 -0.004937457 -0.08133735 0.07347874