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. For regular Bayesian models with suitable priors, BIC approximates minus twice the log marginal likelihood
up to terms that remain bounded as 
grows. It imposes a larger penalty for additional parameters
than the Akaike information criterion
when 
.
