Bicop.mbic

Bicop.mbic(self, u: numpy.ndarray = array([], shape=(0, 2), dtype=float64), psi0: float = 0.9) → float

Evaluates the modified Bayesian information criterion (mBIC).

The mBIC is defined as

\[\mathrm{BIC} = -2\, \mathrm{loglik} + p \log(n) - 2 (I \log(\psi_0) + (1 - I) \log(1 - \psi_0),\]

where \(\mathrm{loglik}\)is the log-liklihood (see loglik()), \(p\)is the (effective) number of parameters of the model, and \(\psi_0\)is the prior probability of having a non-independence copula and \(I\)is an indicator for the family being non-independence.

Parameters:

undarray, shape (n, m), dtype float

An \(n \times (2 + k)\)matrix of observations contained in \((0, 1)\), where \(k\)is the number of discrete variables.

psi0float

Prior probability of a non-independence copula.

Returns:

float

The mBIC evaluated at u.