bayes_posterior

std.stats.bayes_posterior · Level L0

Bayes' theorem on a finite partition of hypotheses: the posterior P(Hᵢ | E) = P(Hᵢ)·P(E | Hᵢ) / Σⱼ P(Hⱼ)·P(E | Hⱼ). The evidence in the denominator is the law of total probability, and it must be positive.

P(Hᵢ | E) = P(Hᵢ)P(E | Hᵢ) / Σⱼ P(Hⱼ)P(E | Hⱼ)

Signature

bayes_posterior(prior: f64[k], likelihood: f64[k]) → f64[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 prior*likelihood / sum(prior*likelihood) in exact rational arithmetic, on all 40 test cases.
All 163 float64 results inside the running error bound; the closest uses 45% 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 42% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 77%
bit-equal to the NumPy formula in float64: 91%
largest error, in units in the last place: 2.59

Identity

Calls

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Called by

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sha256:d6bc74ca8b2d052346ed9abf4a59578dc7c404a75b788213429e44e8b4555597

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.bayes_posterior · Ω:bayes_posterior
Pins: sha256:f2b230e80cd6c40d62b9663dfdecf039af1896cf5f79686072aee866c60fdc02this graph alone
Evidence: sha256:8b6b3cec9b9c3717c2d616d99d3257f8ef85949f98765e60ce2ad6da2add6d39the 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.