Likelihoods and priors

A likelihood is the noise model of a measurement, and a prior states what is known about a parameter before the data. See statistical estimation.

Likelihoods

Pass one as likelihood= of a Measurement.

diff_soup.inference.Gaussian

Independent Gaussian noise with standard deviation sigma.

Pass sigma, or scale in its place, but not both.

Parameters:

Name	Type	Description	Default
sigma		The standard deviation, one value or one per entry of the measured values.	None
scale		Another name for sigma.	None

diff_soup.inference.CorrelatedGaussian

Gaussian noise correlated across the values of one time, with covariance cholesky @ cholesky.T.

For a measurement with one value per time, a factor with one row per time correlates the times instead.

Parameters:

Name	Type	Description	Default
cholesky		The lower Cholesky factor of the covariance, one row per value of a time.	required

diff_soup.inference.StudentT

Independent Student-t noise with df degrees of freedom and scale scale.

It tolerates outliers, and approaches Gaussian noise of standard deviation scale as df grows.

Parameters:

Name	Type	Description	Default
df		The degrees of freedom, positive, one value or one per entry of the measured values.	required
scale		The scale of the noise, positive, one value or one per entry.	required

diff_soup.inference.Poisson

Independent Poisson noise of counts, with expected count exposure times the predicted value.

The observed values must be counts, non-negative integers.

Parameters:

Name	Type	Description	Default
exposure		The positive factor from predicted value to expected count, one value or one per entry, by default 1.0.	required

diff_soup.inference.LogNormal

Independent log-normal noise, with the logarithm of each value Gaussian of standard deviation scale.

The predicted value is the mean of the observed value, and both must be positive.

Parameters:

Name	Type	Description	Default
scale		The standard deviation of the logarithm, positive, one value or one per entry.	required

diff_soup.inference.MultiplicativeGaussian

Independent Gaussian noise with standard deviation scale times the absolute predicted value.

An observed value of zero is refused unless its time is masked out.

Parameters:

Name	Type	Description	Default
scale		The relative standard deviation, positive, one value or one per entry.	required

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Priors

A MAP fit needs one on every fitted parameter handle.

diff_soup.inference.NormalPrior dataclass

A normal prior with mean mean and standard deviation scale.

Declare it as prior= of spec.param or spec.function, for a MAP fit.

Parameters:

Name	Type	Description	Default
mean	Any	The mean, one value or one per entry of the parameter.	required
scale	Any	The standard deviation, positive, one value or one per entry.	required

diff_soup.inference.LogNormalPrior dataclass

A log-normal prior with median median and standard deviation log_sd of the logarithm.

Declare it as prior= of spec.param, for a MAP fit of a positive parameter.

Parameters:

Name	Type	Description	Default
median	Any	The median, positive, one value or one per entry of the parameter.	required
log_sd	Any	The standard deviation of the parameter's logarithm, positive, one value or one per entry.	required

diff_soup.inference.GaussianCoefficientPrior dataclass

A normal prior on the coefficients of a function, centered on its declared coefficients.

Declare it as prior= of spec.function, for a MAP fit. Coefficient n, counted from 0, has standard deviation scale / (1 + n * (n + 1)) ** (smoothness / 2).

Parameters:

Name	Type	Description	Default
scale	float	The standard deviation of the first coefficient, positive.	required
smoothness	float	How fast the standard deviation falls with the coefficient index, non-negative.	2.0