estimator_mse
std.stats.estimator_mse · Level L0The mean squared error of an estimator T under its finite sampling law at θ, computed directly: Σ pᵢ(tᵢ − θ)². It equals bias² + variance, a theorem the tests check rather than the definition used. MSE = 0 exactly when T = θ almost surely.
Signature
estimator_mse(p: f64[k], t: f64[k], theta: f64[]) → f64[]
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
sum(p*(t - theta)**2)in exact rational arithmetic, on all 40 test cases. - All 40 float64 results inside the running error bound; the closest uses 46% 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 45% of it.
- correctly rounded (the float64 nearest the exact value)
- 75%
- bit-equal to the NumPy formula in float64
- 95%
- largest error, in units in the last place
- 1.79
Identity
sha256:41331738264b6865fc94b5ce38c07908ecd3a7a7afb4d853a3468a7754faf11cThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.stats.estimator_mse · Ω:estimator_mse
- Pins
sha256:6ed31c61fc5a6c23fd4214be932fef36c372bc16135bb02ae624f2d3b3b40f5fthis graph and the 1 it reaches through calls- Evidence
sha256:b020aebb17bc441d10e6405ccce7920f2269694349b6bcf379c53c697f0924e8the 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.