finite_mle

std.stats.finite_mle · Level L2

The maximum-likelihood estimator on a finite parametric model, one law P_θ per row: for every possible sample x, the likelihood θ ↦ P_θ(x) is maximized over all θ, and the estimate is the first θ attaining it, a fixed tie order that does not depend on the unknown θ. Also the maximal likelihood, whether there is a tie, and whether every likelihood is 0 there. The MLE maximizes the likelihood, not a posterior; it need not be unique, unbiased or consistent.

θ̂(x) = argmax_θ P_θ(x)

Signature

finite_mle(P: f64[r, n]) → f64[n], f64[n], f64[n], f64[n]

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 first largest entry of each column, its value, ties and zeros in exact rational arithmetic, on all 40 test cases.
All 564 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

—

Called by

—

sha256:8f0ad5297bac34a204319d7ae60286934cea98aec58e16334ded4da42c3d2fe4

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.finite_mle · Ω:finite_mle
Pins: sha256:928c33b38922a66b2afb54c72e904772981c850978f8bce53d2091b2a25bf726this graph alone
Evidence: sha256:e30f4f00765efe9d4dc74c556824660974867c157555bf0f4ef783dddb06ea4dthe 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.