ci_coverage

std.stats.ci_coverage · Level L1

The coverage of an interval procedure [L(x), U(x)], fixed for every possible sample x before the data are seen, over a finite family of laws P_θ (one row per θ, with the θ values given): for each θ, Σ_x P_θ(x)·[L(x) ≤ θ ≤ U(x)], and the worst case, the minimum over θ. A high average coverage does not make the worst case high, and coverage is not a posterior probability. A selection rule must be part of the procedure before coverage is computed.

C(θ) = Σ_x P_θ(x)·[L(x) ≤ θ ≤ U(x)]; min_θ C(θ)

Signature

ci_coverage(P: f64[r, n], theta: f64[r], L: f64[n], U: f64[n]) → f64[r], f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the mass of the samples whose interval contains θ, per θ in exact rational arithmetic, on all 40 test cases.
All 188 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:3f4c310f287e3049ba5bd6d111e31da62f26b6cf114badb3e95628f6e2fbc459

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.stats.ci_coverage · Ω:ci_coverage
Pins: sha256:dea55ad244fd3e6bd2a668cc975b2d032bf4205a3305e2d14b0fd41deddf5108this graph alone
Evidence: sha256:0373fd5ce848a98901d8e9ccbc8788f925f429a8f6ac26319032c7ccc98fcf6athe hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.