smile.stat.distribution

Class BIC

java.lang.Object

smile.stat.distribution.BIC

public class BIC
extends java.lang.Object

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.

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.

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.

Given any two estimated models, the model with the larger value of BIC is the one to be preferred.

Constructor Summary

Constructors

Constructor and Description
BIC()

Method Summary

Modifier and Type	Method and Description
static double	bic(double L, int v, int n) Returns the BIC score of an estimated model.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BIC

public BIC()

Method Detail

bic

public static double bic(double L,
                         int v,
                         int n)

Returns the BIC score of an estimated model.

Parameters:

L - the log-likelihood of estimated model.

v - the number of free parameters to be estimated in the model.

n - the number of samples.

Returns:

BIC score.