pushforward

std.stats.pushforward · Level L3

The law of a random variable X on a finite sample space, for one law or a family of laws (one per row of P): P(X = t) = Σ over the outcomes s with X(s) = t of P(s). With a statistic T and a parametric family P_θ it is T's sampling distribution, one row per θ. X is given by value indices into 0 … k − 1 (a carrier vector of length k, only its length read). It is not a likelihood or a posterior.

P(X = t) = Σ_{s : X(s) = t} P(s)

Signature

pushforward(P: f64[r, n], X: i64[n], cod: f64[k]) → f64[r, k]

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 masses of the outcomes with each value, summed in exact rational arithmetic, on all 40 test cases.
All 647 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

fiber_conditional

sha256:41a1dfb364ea8db7679062ee864f162c6d2bd441b6636d8bc79e25e379d89261

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.pushforward · Ω:pushforward
Pins: sha256:5c318b295f21cf0f3403218189ee82e245a116d8f3ed9b3ed1f865ca8e5b4ddfthis graph alone
Evidence: sha256:62624d1194f32f3e59bf2a01f88fedc0fef41af7504d1ba683455868bd485369the 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.