Sawa's bayesian information criterionSource:
Sawa's bayesian information criterion for model selection.
Sawa (1978) developed a model selection criterion that was derived from a Bayesian modification of the AIC criterion. Sawa's Bayesian Information Criterion (BIC) is a function of the number of observations n, the SSE, the pure error variance fitting the full model, and the number of independent variables including the intercept.
$$SBIC = n * ln(SSE / n) + 2(p + 2)q - 2(q^2)$$
where \(q = n(\sigma^2)/SSE\), n is the sample size, p is the number of model parameters including intercept SSE is the residual sum of squares.
Sawa, T. (1978). “Information Criteria for Discriminating among Alternative Regression Models.” Econometrica 46:1273–1282.
Judge, G. G., Griffiths, W. E., Hill, R. C., and Lee, T.-C. (1980). The Theory and Practice of Econometrics. New York: John Wiley & Sons.