estimator_expectations

std.stats.estimator_expectations · Level L0

The expectation E_θ[T] of a statistic T (its value t(x) on each sample x, never indexed by θ) under every law of a finite parametric family, one per row: the vector P·t. It says nothing by itself about bias, consistency or sufficiency.

E_θ[T] = Σ_x P_θ(x) t(x)

Signature

estimator_expectations(P: f64[r, n], t: f64[n]) → f64[r]

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 each row dotted with t in exact rational arithmetic, on all 40 test cases.
All 175 float64 results inside the running error bound; the closest uses 48% 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 55% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 90%
bit-equal to the NumPy formula in float64: 91%
largest error, in units in the last place: 3.75

Identity

Calls

matvec

Called by

—

sha256:a3b65c2056c0ccdc6560e34003d5c343b2f7b6111a3b3bc6b8b674ae41adf90e

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_expectations · Ω:estimator_expectations
Pins: sha256:3039e9dd91b54318298dbee828cb65003d1b404f9a50018770176ce62e1ca1e5this graph and the 1 it reaches through calls
Evidence: sha256:c2e03453366ddf56cd1b00848d821224562e6f617a5068ba8872992048232c31the 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.