The Schwarz Criterion

What is the Schwarz Criterion?

The Schwarz Criterion is an index to help quantify and choose the least complex probability model among multiple options. Also called the Bayesian Information Criterion (BIC), this approach ignores the prior probability and instead compares the efficiencies of different models at predicting outcomes. That efficiency is measured by creating an index of each model’s parameters using a likelihood function, and then applying a penalizing function for models with more parameters.

How to Use the Schwarz Criterion?

The BIC or SC is expressed as:

SC = log(n) k – 2 log(L(θ̂))

n = sample size

k = number of parameters being estimated

θ = set of all parameter values

L(θ̂) = likelihood of the model returning the data you have, when tested at the maximum likelihood values of θ. The best-case scenario.

Repeat this procedure for each model, and choose the one with the lowest SC/BIC score to achieve maximum efficiency.