csep.core.catalog_evaluations.resampled_magnitude_test

csep.core.catalog_evaluations.resampled_magnitude_test(forecast: CatalogForecast, observed_catalog: CSEPCatalog, verbose: bool = False, seed: int | None = None) → CatalogMagnitudeTestResult

Performs the resampled magnitude test for catalog-based forecasts (Serafini et al., 2024), which corrects the bias from the original M-test implementation to the total N of events. Calculates the (pseudo log-likelihood) test statistic distribution from the forecast’s synthetic catalogs Λ_j as:

D_j = Σ_k [log(Λ_u(k) * N / N_u + 1) - log(Λ̃_j(k) + 1)] ^ 2

where k are the magnitude bins, Λ_u the union of all synthetic catalogs, N_u the total number of events in Λ_u, and Λ̃_j the resampled catalog containing exactly N events.

The pseudo log-likelihood statistic from the observations is calculated as:

D_o = Σ_k [log(Λ_U(k) * N / N_u + 1) - log(Ω(k) + 1)]^2

where Ω is the observed catalog.

Parameters:

• forecast (CatalogForecast) – The forecast to be evaluated

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

• 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.