estimator_bias

std.stats.estimator_bias · Level L0

The bias E_θ[T] − θ of an estimator T whose finite sampling law under θ gives the value tᵢ the probability pᵢ.

bias = Σ pᵢtᵢ − θ

Signature

estimator_bias(p: f64[k], t: f64[k], theta: f64[]) → 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) - theta in exact rational arithmetic, on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 55% 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 61% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 88%
bit-equal to the NumPy formula in float64: 90%
largest error, in units in the last place: 12

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls

dot

Called by

—

sha256:41a0aae00f77d639bc65a45d26b5983bc94e183c08f3e78c57d0b0dab834d499

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_bias · Ω:estimator_bias
Pins: sha256:d87c11b7657c46fee33aaf4fa15a3aed4f151c7980a0048524a049d10de4226ethis graph and the 1 it reaches through calls
Evidence: sha256:bd2fd8280cb928a9345128a04cc2facf2a3d05d509d1a05446c8a6d179655098the 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.