Manuscript En10-B@1 · En10-B.tex · section · a1105bad

Finite nuisance and calibration set

The frozen finite source and generator model › Finite nuisance and calibration set · lines 290–326

En10-B@1#eq:calibration-set

Fix a positive integer $m$ . A nuisance value is

η = (ϕ, γ, n, ξ_{1}, \dots, ξ_{m}, w_{1}, \dots, w_{m}),

where

n = (n_{x}, n_{y}, n_{z}) \in S^{2}, w_{k} \geq 0, k = 1 \sum^{m} w_{k} = 1.

A fresh hidden label $k$ is drawn with probabilities $w_{k}$ on each trial, independently of the source input. It selects one kick, not an unrecorded adaptive stopping rule.

Freeze a nonempty compact calibration set $K$ satisfying

0 \leq γ_{-} \leq γ \leq γ_{+} < 1, ∣ ϕ - ϕ_{0} ∣ \leq ϵ_{ϕ}, ∣ ξ_{k} ∣ \leq κ, ∣ n_{z} ∣ \leq z_{*} < 1, 0 < ϕ_{0} - ϵ_{ϕ} - κ, ϕ_{0} + ϵ_{ϕ} + κ < \frac{π}{4} .

The nominal loss is $γ_{0} \in [γ_{-}, γ_{+}]$ , and

ϵ_{γ} = η \in K sup ∣ γ - γ_{0} ∣.

The set may impose additional correlations among its variables. A rectangular calibration set is not required.

The finite list $(ξ_{k}, w_{k})$ is a random-kick nuisance model. It is not an exact continuum turbulence spectrum.

Displayed formulas in this passage

En10-B@1#eq:calibration-set · line 306
$0 \leq γ_{-} \leq γ \leq γ_{+} < 1, ∣ ϕ - ϕ_{0} ∣ \leq ϵ_{ϕ}, ∣ ξ_{k} ∣ \leq κ, ∣ n_{z} ∣ \leq z_{*} < 1, 0 < ϕ_{0} - ϵ_{ϕ} - κ, ϕ_{0} + ϵ_{ϕ} + κ < \frac{π}{4} .$
unlabeled · line 293
$η = (ϕ, γ, n, ξ_{1}, \dots, ξ_{m}, w_{1}, \dots, w_{m}),$
unlabeled · line 297
$n = (n_{x}, n_{y}, n_{z}) \in S^{2}, w_{k} \geq 0, k = 1 \sum^{m} w_{k} = 1.$
unlabeled · line 317
$ϵ_{γ} = η \in K sup ∣ γ - γ_{0} ∣.$