Calibration of the dominance noise (sigma_nu and n)
Source:R/calibration_dominance.R
pm_calib_dominance.RdTheoretical, data-free. For every candidate (sigma_nu, n, beta, sigma_eps),
evaluates the scenario-I risk over an internal grid of dominance levels
rho, keeps its worst case (max over rho), and reports the maximum
information loss (reached at rho = 1, hence set by sigma_nu alone). The
returned table is the decision surface of step 2: feed it to plot() for the
risk heat-map, to pm_suggest_n() for the largest admissible n, then lock
the choice with pm_commit_dominance().
Usage
pm_calib_dominance(
params = NULL,
sigma_nu = NULL,
n = NULL,
beta = NULL,
sigma_eps = NULL,
level = 0.95,
rho = NULL
)Arguments
- params
Optional
pm_params. When supplied,sigma_epsandbetadefault to its values.- sigma_nu, n
Numeric vectors of candidate values. Default to
(1:5) / 10andseq(3, 12, by = 3).- beta
Accuracy threshold(s) of scenario I. Default to the
dominancepolicy ofparams, or toc(0.1, 0.2).- sigma_eps
Fixed differencing noise. Default to
params$mechanism$sigma_eps, or0when noparamsis given.- level
Confidence level for the CI loss metric (default 0.95).
- rho
Internal grid of dominance levels used to locate the worst case. Default
(1:50) / 50.
Value
A data.frame of class pm_calib_dominance, one row per
(rho, sigma_nu, sigma_eps, n, beta), with columns risk (scenario-I
risk), EZ and CI (information loss, in percent). The confidence level
is stored in the level attribute. Use summary() for the worst case
over rho of each parameter combination.
Details
Like pm_calib_diff(), calling it with everything at NULL returns a
default exploration grid.
Examples
# default exploration
grid <- pm_calib_dominance()
grid
#> <pm_calib_dominance> 2000 rows (rho-resolved)
#> rho : 50 values in [0.02, 1]
#> sigma_nu : 5 values in [0.1, 0.5]
#> n : 4 values in [3, 12]
#> beta : 0.1, 0.2
#> sigma_eps: 0
#> CI level : 95%
#>
#> worst-case risk & loss range per combination (40 total):
#> sigma_nu sigma_eps n beta rho_at_max_risk risk_max EZ_min EZ_max CI_min
#> 0.1 0 3 0.1 0.98 0.691 0 7.979 0
#> 0.1 0 3 0.2 0.98 0.958 0 7.979 0
#> 0.1 0 6 0.1 0.96 0.722 0 7.979 0
#> 0.1 0 6 0.2 0.96 0.972 0 7.979 0
#> 0.1 0 9 0.1 0.96 0.766 0 7.979 0
#> 0.1 0 9 0.2 0.94 0.987 0 7.979 0
#> 0.1 0 12 0.1 0.96 0.806 0 7.979 0
#> 0.1 0 12 0.2 0.90 0.998 0 7.979 0
#> CI_max
#> 19.6
#> 19.6
#> 19.6
#> 19.6
#> 19.6
#> 19.6
#> 19.6
#> 19.6
#> ... 32 more; call summary() for the full digest.
summary(grid)
#> sigma_nu sigma_eps n beta rho_at_max_risk risk_max EZ_min EZ_max CI_min
#> 0.1 0 3 0.1 0.98 0.691 0 7.979 0.000
#> 0.1 0 3 0.2 0.98 0.958 0 7.979 0.000
#> 0.1 0 6 0.1 0.96 0.722 0 7.979 0.000
#> 0.1 0 6 0.2 0.96 0.972 0 7.979 0.000
#> 0.1 0 9 0.1 0.96 0.766 0 7.979 0.000
#> 0.1 0 9 0.2 0.94 0.987 0 7.979 0.000
#> 0.1 0 12 0.1 0.96 0.806 0 7.979 0.000
#> 0.1 0 12 0.2 0.90 0.998 0 7.979 0.000
#> 0.2 0 3 0.1 0.94 0.404 0 15.958 0.000
#> 0.2 0 3 0.2 0.94 0.712 0 15.958 0.000
#> 0.2 0 6 0.1 0.94 0.465 0 15.958 0.000
#> 0.2 0 6 0.2 0.92 0.790 0 15.958 0.000
#> 0.2 0 9 0.1 0.94 0.527 0 15.958 0.000
#> 0.2 0 9 0.2 0.92 0.862 0 15.958 0.000
#> 0.2 0 12 0.1 0.94 0.587 0 15.958 0.000
#> 0.2 0 12 0.2 0.90 0.922 0 15.958 0.000
#> 0.3 0 3 0.1 0.92 0.290 0 23.937 0.000
#> 0.3 0 3 0.2 0.92 0.543 0 23.937 0.000
#> 0.3 0 6 0.1 0.90 0.358 0 23.937 0.000
#> 0.3 0 6 0.2 0.90 0.653 0 23.937 0.000
#> 0.3 0 9 0.1 0.92 0.421 0 23.937 0.000
#> 0.3 0 9 0.2 0.90 0.746 0 23.937 0.000
#> 0.3 0 12 0.1 0.92 0.484 0 23.937 0.000
#> 0.3 0 12 0.2 0.90 0.827 0 23.937 0.000
#> 0.4 0 3 0.1 0.88 0.231 0 31.915 0.001
#> 0.4 0 3 0.2 0.88 0.443 0 31.915 0.001
#> 0.4 0 6 0.1 0.88 0.300 0 31.915 0.000
#> 0.4 0 6 0.2 0.88 0.563 0 31.915 0.000
#> 0.4 0 9 0.1 0.90 0.364 0 31.915 0.000
#> 0.4 0 9 0.2 0.90 0.662 0 31.915 0.000
#> 0.4 0 12 0.1 0.90 0.418 0 31.915 0.000
#> 0.4 0 12 0.2 0.90 0.754 0 31.915 0.000
#> 0.5 0 3 0.1 0.86 0.194 0 39.894 0.001
#> 0.5 0 3 0.2 0.86 0.377 0 39.894 0.001
#> 0.5 0 6 0.1 0.86 0.263 0 39.894 0.000
#> 0.5 0 6 0.2 0.86 0.501 0 39.894 0.000
#> 0.5 0 9 0.1 0.88 0.326 0 39.894 0.000
#> 0.5 0 9 0.2 0.88 0.608 0 39.894 0.000
#> 0.5 0 12 0.1 0.90 0.383 0 39.894 0.000
#> 0.5 0 12 0.2 0.88 0.695 0 39.894 0.000
#> CI_max
#> 19.600
#> 19.600
#> 19.600
#> 19.600
#> 19.600
#> 19.600
#> 19.600
#> 19.600
#> 39.199
#> 39.199
#> 39.199
#> 39.199
#> 39.199
#> 39.199
#> 39.199
#> 39.199
#> 58.799
#> 58.799
#> 58.799
#> 58.799
#> 58.799
#> 58.799
#> 58.799
#> 58.799
#> 78.399
#> 78.399
#> 78.399
#> 78.399
#> 78.399
#> 78.399
#> 78.399
#> 78.399
#> 97.998
#> 97.998
#> 97.998
#> 97.998
#> 97.998
#> 97.998
#> 97.998
#> 97.998
# at a committed sigma_eps
para <- pm_commit_diff(pm_params())
#> Differencing step committed: beta = 0.05, tau = 0.95 -> sigma_eps = 0.0255
#> loss floor at rho -> 0: E|Z| = 2.04%, upper 95% CI = 5.00%
grid <- pm_calib_dominance(para)