Fit a noise model

Compute the residuals

A residual is what the sensor added or scaled on top of the truth. For a ground truth $g$ and a sensor reading $y$, the additive residual is $y - g$ and the multiplicative residual is $y / g$. NoiseModel.residuals computes the vector of residuals from the two aligned slices.

from sentil import NoiseInteraction, NoiseModel

truth = [1.0, 2.0, 3.0, 4.0]
sensor = [1.1, 1.9, 3.2, 3.8]
resid = NoiseModel.residuals(truth, sensor, NoiseInteraction.Additive)

use sentil::{NoiseInteraction, NoiseModel};

let truth = [1.0, 2.0, 3.0, 4.0];
let sensor = [1.1, 1.9, 3.2, 3.8];
let resid = NoiseModel::residuals(&truth, &sensor, NoiseInteraction::Additive)?;

Pick the interaction mode

If you don't really know whether the sensor behaves additively or multiplicatively, compute both residuals and plot them against the ground-truth values. Then, the interaction whose residuals show no trend against the truth is the one you pick because the fitted distribution describes the same noise at every reading. Which sensors behave additively and which multiplicatively is on the noise-models concept page.

Choose the distribution family

With the interaction mode fixed, the residual histogram decides the family, and the table maps each shape to its fitter. You can always add new distribution families to the library or you can construct one from the distribution catalog rather than fit the ones we have.

Fit and register

Each fitter is a free function on NoiseModel that takes the residual samples and returns a model ready to register.

gaussian = NoiseModel.fit_gaussian(resid)              # symmetric bell
empirical = NoiseModel.fit_bootstrap(resid)            # resample as-is
thinned = NoiseModel.fit_bootstrap_reservoir(resid, 2000)
bimodal = NoiseModel.fit_gaussian_mixture(resid, 2, 100)  # 2 modes, 100 EM iters

let gaussian = NoiseModel::fit_gaussian(&resid)?;
let empirical = NoiseModel::fit_bootstrap(&resid)?;
let thinned = NoiseModel::fit_bootstrap_reservoir(&resid, 2000)?;
let bimodal = NoiseModel::fit_gaussian_mixture(&resid, 2, 100)?;

fit_gaussian fits by maximum likelihood with the Bessel-corrected variance, so it needs at least two samples. fit_bootstrap keeps every residual and draws from them with replacement. fit_bootstrap_reservoir caps the model at max_samples residuals by seeded reservoir sampling. fit_gaussian_mixture runs expectation-maximization for up to max_iters steps, seeds the component means from equal-size sorted chunks, and returns a mixture of Gaussians.