process_marginals

std.stats.process_marginals · Level L3

The one-time marginals of a discrete-time process on a finite horizon, given by the complete list of its paths (each a row of state indices over the times) and their probabilities: P(X_t = s) for every time t and state s. A finite-horizon joint law gives the marginals and the two-time joints; it does not by itself give the Markov property or stationarity.

P(X_t = s) = Σ_paths p(ω)·[ω_t = s]

Signature

process_marginals(paths: i64[N, T], p: f64[N], states: f64[k]) → f64[T, 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 paths in each state at each time in exact rational arithmetic, on all 40 test cases.
All 556 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

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Called by

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sha256:c4e45c2289ea495ebddea89be7bb0f6f2d0dd802a9f311abcfa67d97e4f0aef6

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.process_marginals · Ω:process_marginals
Pins: sha256:c59d02c34273741f1e2da30e1578a4b694af6a2b2857a96d137781090e2f8079this graph alone
Evidence: sha256:f89cc31485c6fdef29527d0f538ee47349e1900b5c6519f0a7935d965ce1ccf9the 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.