rxmc.likelihood_model.UnknownModelError

class rxmc.likelihood_model.UnknownModelError(averaging=True)

Bases: ParametricLikelihoodModel

A ParametricLikelihoodModel in which the frac_err is a free parameter $gamma$, such that the covariance due to the uncorrelated model error takes the form:

\[\Sigma_{ij}^{uncorrelated} = \gamma^2 y_m(x_i, \alpha)^2 \delta_{ij}\]

where $gamma$ is a free parameter.

This is commonly used as a model-error term or unquantified uncertainty.

__init__(averaging=True)

Initializes the UnknownModelError instance.

Parameters:

averaging (bool, optional) – If True, the model error term uses 0.5 * (observation.y + ym) instead of ym alone, which improves stability when ym is near zero. Defaults to True.

Methods

__init__([averaging])	Initializes the UnknownModelError instance.
chi2(observation, ym, *likelihood_params)	Calculate the generalised chi-squared statistic.
covariance(observation, ym, log_frac_err)	Default covariance model.
log_likelihood(observation, ym, ...)	Returns the log likelihood that ym reproduces observation.y
residual(observation, ym)	Return the residual observation.y - ym.

covariance(observation: Observation, ym: ndarray, log_frac_err: float)

Default covariance model. Derived classes of LikelihoodModel will override this.

Returns the following covariance matrix:

\[\Sigma_{ij} = \sigma^2_{i}^{stat} \delta_{ij} + \Sigma_{ij}^{sys} + \gamma^2 y_m^2(x_i, \alpha)\]

where $gamma$ is the fractional uncorrelated error (frac_err), treated here as a free parameter, and all other definitions are the same as LikelihoodModel.covariance

Parameters:

• ym (np.ndarray) – Model prediction for the observation.

• observation (Observation) – The observation object containing the observed data.

• log_frac_err (float) – log of fraction of the model prediction at point x_i that is treated as the standard deviation of the model prediction at that point, such that the model prediction is independent at every point (log of $gamma$).

Returns:

np.ndarray – Covariance matrix of the observation.