The Bayesian information criterion (BIC), also called the Schwarz criterion, is a criterion for comparing statistical models fitted to the same data. If 
is the maximized likelihood,
is the number of estimated parameters, and 
is the number of observations, it is defined by
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The model with the smallest BIC is preferred. Under regularity conditions, the criterion is an asymptotic approximation to a Bayesian model comparison and imposes a larger
penalty for additional parameters than the Akaike
information criterion when 
.
