pint.utils.bayesian_information_criterion

pint.utils.bayesian_information_criterion(model: pint.models.timing_model.TimingModel, toas: pint.toas.TOAs) → float[source]

Compute the Bayesian information criterion (BIC). The BIC is used for comparing different models for the given dataset.

Given a model with best-fit parameters, the AIC is defined as

BIC = k*ln(N) - 2*ln(L)

where k is the number of free parameters in the model, N is the number of data points/samples, and L is the maximum value of the likelihood for the model.

Given n models with BIC values BIC1, …, BICn, the preferred model is the one that minimizes the BIC value.

The BIC is an approximation for the Bayesian evidence. It is computed by Taylor-expanding the log-likelihood function up to the second order in the vicinity of the maximum-likelihood point and assuming that the prior distribution doesn’t vary appreciably in this neighbourhood.

See, e.g., Burnham & Anderson 2004 for further details.

Unlike the F-test (:function:`~pint.utils.FTest`), the BIC does not require the models to be nested.

See also :function:`~pint.utils.akaike_information_criterion` for the Akaike Information Criterion (AIC), a similar quantity used for model comparison. The main practical difference between AIC and BIC is that the BIC more heavily penalizes the number of free parameters.

Parameters:
Returns:

bic – The Bayesian information criterion

Return type:

float