Calibrate p-values into e-values

Convert one or more p-values into e-values using simple, standard p-to-e calibration rules from the e-value literature (e.g. Vovk & Wang, 2021; Ramdas et al., 2025). An e-value is a nonnegative statistic with expectation at most 1 under the null; large values indicate evidence against the null. oai_citation:2‡Project Euclid

This helper is primarily used internally by DrBristol but is exported for convenience.

Usage

e_from_p(p, method = c("inverse", "kappa"), kappa = 0.5, cap = Inf)

Arguments

p

Numeric vector of p-values in (0,1]. Values \(\le 0\) or \(> 1\) are not allowed and will trigger an error.

method

Character scalar specifying the calibration rule:

• "inverse": returns \(e = 1/p\). This is often used informally as an "e-like" evidence measure. Note that for a generic valid p-variable this may not be a mathematically valid e-variable in the strict Ramdas–Vovk sense; it is, however, a monotone transform with the usual interpretation that larger values indicate more evidence against the null.

• "kappa": Vovk–Wang admissible κ-calibrator \(e = \kappa p^{\kappa-1}\), with \(0 < \kappa < 1\). This does yield a proper e-variable when applied to a valid p-variable. oai_citation:3‡Wikipedia

kappa

Numeric scalar in (0,1). Only used when method = "kappa".

cap

Optional numeric upper cap for the returned e-values (e.g., to avoid overflow when p is extremely small). Default Inf means no capping.

Value

A numeric vector of e-values of the same length as p.

Examples

e_from_p(0.05) # 1/p style
#> [1] 20
e_from_p(c(0.1, 0.01)) # vectorised
#> [1]  10 100
e_from_p(0.05, method = "kappa", kappa = 0.5)
#> [1] 2.236068