estimator_variance

std.stats.estimator_variance · Level L0

The variance of an estimator T under its finite sampling law: Σ pᵢ(tᵢ − E[T])².

Var(T) = Σ pᵢ(tᵢ − E[T])²

Signature

estimator_variance(p: f64[k], t: f64[k]) → 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 sum(p*(t - E[T])**2) in exact rational arithmetic, on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 23% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 18% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 68%
bit-equal to the NumPy formula in float64: 93%
largest error, in units in the last place: 1.63

Identity

Calls

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Called by

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sha256:3aafbbdab98a08477bdf9127c8b472583fb8c66d344ba96d9a957cb0aff7ebee

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.estimator_variance · Ω:estimator_variance
Pins: sha256:54e8170ec4405ca897dc6c1816be2ab67311060c7992a4b50e97c6daf603716dthis graph and the 1 it reaches through calls
Evidence: sha256:7c91c78fffe6517884833fdb1e96bc0e108d298711e7355539dce87b9d408e1cthe 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.