csep.core.catalog_evaluations.MLL_magnitude_test

csep.core.catalog_evaluations.MLL_magnitude_test(forecast: CatalogForecast, observed_catalog: CSEPCatalog, full_calculation: bool = False, verbose: bool = False, seed: int | None = None) → CatalogMagnitudeTestResult[source]

Implements the modified Multinomial log-likelihood ratio (MLL) magnitude test (Serafini et al., 2024). Calculates the test statistic distribution as:

D̃_j = -2 * log( L(Λ_u + N_u / N_j + Λ̃_j + 1) /

[L(Λ_u + N_u / N_j) * L(Λ̃_j + 1)] )

where L is the multinomial likelihood function, Λ_u the union of all the forecasts’ synthetic catalogs, N_u the total number of events in Λ_u, Λ̃_j the resampled catalog containing exactly N observed events. The observed statistic is defined as:

D_o = -2 * log( L(Λ_u + N_u / N + Ω + 1) /

[L(Λ_u + N_u / N) * L(Ω + 1)] )

where Ω is the observed catalog.

Parameters:

  • forecast (CatalogForecast) – The forecast to be evaluated

  • observed_catalog (CSEPCatalog) – The observation/testing catalog.

  • full_calculation (bool) – Whether to sample from the entire stochastic catalogs or from its already processed magnitude histogram.

  • verbose (bool) – Flag to display debug messages

  • seed (int) – Random number generator seed

Returns:

A CatalogMagnitudeTestResult object containing the statistic distribution and the observed statistic.