fiber_conditional

std.stats.fiber_conditional · Level L3

Sufficiency of a statistic T on a finite parametric model: the conditional law P_θ(x | T = T(x)) for every θ and sample x (0 on a zero-mass cell, where it is undefined), and for each x the spread of that conditional probability across the θ for which its cell has positive mass. T is sufficient exactly when every spread is 0: within each fibre of T the conditional law does not depend on θ. The factorization theorem is not used.

P_θ(x | T = T(x)) independent of θ

Signature

fiber_conditional(P: f64[r, n], T: i64[n], cod: f64[k]) → f64[r, 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 conditional masses per fibre, and their range over θ, in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 738 float64 results inside the running error bound; the closest uses 13% 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): 96%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 5.66

Identity

Calls

pushforward

Called by

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sha256:7d034541cb1b3b4a5938c0a0699dfcc720b42afd30ca0ad1345de0f4cb62170e

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.fiber_conditional · Ω:fiber_conditional
Pins: sha256:90eabcec386aec8ab05ac15a9e0fa94e4774c20028c07812c5ae001f60c155b4this graph and the 1 it reaches through calls
Evidence: sha256:28a54a81a93680e3b6a1f22022023b9577fac17621d6016e17e2d3d279087cf5the 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.