Every noise family SENTIL can lift a trace with, its parameters and constructor, the additive and multiplicative interactions, and the fitters that build a model from paired calibration data.

A probabilistic specification asks how a property fares once sensor readings are perturbed by noise. A NoiseModel is the distribution that noise is drawn from, and a NoiseInteraction says how the draw combines with the reading. Lifting turns each reading into an ensemble of candidate values that the robustness engine evaluates. Every constructor validates its parameters; a bad parameter returns an InvalidNoiseModel error naming the family and the reason.

The families

Seventeen families cover the common shapes of sensor error, from a clean point mass to a data-backed empirical distribution.

Family	Constructor	Parameters	Notes
Dirac	`NoiseModel::dirac(value)`	`value`	a point mass, no noise; a baseline
Gaussian	`NoiseModel::gaussian(mean, std_dev)`	`mean`, `std_dev >= 0`	zero std is a point mass at the mean
Uniform	`NoiseModel::uniform(low, high)`	`low <= high`	flat over `[low, high]`
LogNormal	`NoiseModel::log_normal(mu, sigma)`	`mu`, `sigma >= 0`	log-mean and log-std; own mean `exp(mu + sigma^2/2)`
Exponential	`NoiseModel::exponential(lambda)`	`lambda > 0`	rate `lambda`, mean `1/lambda`
Gamma	`NoiseModel::gamma(shape, scale)`	`shape > 0`, `scale > 0`	mean `shape * scale`
Beta	`NoiseModel::beta(alpha, beta)`	`alpha > 0`, `beta > 0`	on `[0, 1]`, mean `alpha/(alpha+beta)`
Weibull	`NoiseModel::weibull(shape, scale)`	`shape > 0`, `scale > 0`	reliability and time-to-failure
Rayleigh	`NoiseModel::rayleigh(scale)`	`scale > 0`	magnitude of a centered 2D Gaussian
Gumbel	`NoiseModel::gumbel(location, scale)`	`location`, `scale > 0`	extreme-value modeling
Cauchy	`NoiseModel::cauchy(location, scale)`	`location`, `scale > 0`	heavy-tailed; mean and variance undefined
StudentT	`NoiseModel::student_t(df, location, scale)`	`df > 0`, `location`, `scale > 0`	approaches Gaussian as `df` grows
TruncatedNormal	`NoiseModel::truncated_normal(mean, std_dev, lower, upper)`	`std_dev > 0`, `lower < upper`	a Gaussian confined to `[lower, upper]`
Poisson	`NoiseModel::poisson(lambda)`	`lambda > 0`	counts, mean `lambda`
Binomial	`NoiseModel::binomial(n, p)`	`n > 0`, `p` in `[0, 1]`	successes in `n` trials, mean `n * p`
Bootstrap	`NoiseModel::bootstrap(residuals)`	non-empty finite `residuals`	resamples observed residuals with replacement
Mixture	`NoiseModel::mixture(weights, components)`	at least one component; one finite weight `>= 0` per component, summing above zero	draws a component by weight, then draws from it; weights need not sum to one

Each model reports its analytic mean() and variance(), returning None for the families that have none: the Cauchy family throughout, Student-t with one degree of freedom for the mean and two or fewer for the variance.

Interaction

NoiseInteraction says how a noise draw combines with a deterministic reading.

Interaction	Combination	Residual it recovers
`Additive`	`reading + noise`	`sensor - truth`
`Multiplicative`	`reading * noise`	`sensor / truth`

The multiplicative residual guards against a near-zero ground truth, which reads as no deviation, so a truth close to zero does not blow up into a divide.

Fitting a model from data

When you have paired ground-truth and sensor observations, fit the model rather than guessing its parameters. NoiseModel::residuals(ground_truth, sensor, interaction) computes the residual series under the chosen interaction, and a fitter turns that series into a model.

Fitter	Builds	Method
`fit_gaussian(samples)`	a Gaussian	maximum likelihood, Bessel-corrected variance
`fit_bootstrap(samples)`	a bootstrap model	resamples the residuals directly
`fit_bootstrap_reservoir(samples, max_samples)`	a thinned bootstrap	reservoir sampling to a fixed size, seeded and reproducible
`fit_gaussian_mixture(samples, components, max_iters)`	a Gaussian mixture	expectation-maximization with log-sum-exp responsibilities

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 residuals = NoiseModel::residuals(&truth, &sensor, NoiseInteraction::Additive)?;
let model = NoiseModel::fit_gaussian(&residuals)?;

Once you have a model, register it against a signal name and lift the trace. LiftingRegistry::register(name, model, interaction) attaches the model, and lift(trace, seed) draws one realization of the ensemble. During a statistical check the ensemble size is SmcConfig.samples, 10,000 by default; that one knob and its neighbors are on the configuration page.

use sentil::{Formula, NoiseInteraction, NoiseModel, Trace};
use sentil::stats::{LiftingRegistry, SmcConfig};

let mut lifting = LiftingRegistry::new();
lifting.register(
    "speed",
    NoiseModel::gaussian(0.0, 0.3)?,
    NoiseInteraction::Additive,
);
let phi = Formula::parse("P>=0.95(G (speed > 5))")?;
let trace = Trace::from_signal([0.0], "speed", [6.0])?;
let result = phi.check(&trace, &lifting, &SmcConfig::default())?;

For the ideas behind choosing and fitting a model, read noise models, fitting noise models, and lifting a trace.

Noise model catalog

The families

Interaction

Fitting a model from data

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