/*******************************************************************************
* Copyright (c) 2010 Haifeng Li
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*******************************************************************************/
package smile.stat.distribution;
/**
* Bayesian information criterion (BIC) or Schwarz Criterion is a criterion for
* model selection among a class of parametric models with different numbers
* of parameters. Choosing a model to optimize BIC is a form of regularization.
* <p>
* When estimating model parameters using maximum likelihood estimation, it
* is possible to increase the likelihood by adding additional parameters,
* which may result in over-fitting. The BIC resolves this problem by
* introducing a penalty term for the number of parameters in the model.
* BIC is very closely related to the Akaike information criterion (AIC).
* However, its penalty for additional parameters is stronger than that of AIC.
* <p>
* The formula for the BIC is BIC = L - 0.5 * v * log n where L is the
* log-likelihood of estimated model, v is the number of free parameters
* to be estimated in the model, and n is the number of samples.
* <p>
* Given any two estimated models, the model with the larger value of BIC is
* the one to be preferred.
*
* @author Haifeng Li
*/
public class BIC {
/**
* Returns the BIC score of an estimated model.
* @param L the log-likelihood of estimated model.
* @param v the number of free parameters to be estimated in the model.
* @param n the number of samples.
* @return BIC score.
*/
public static double bic(double L, int v, int n) {
return L - 0.5 * v * Math.log(n);
}
}