smile.stat

Class Stat

java.lang.Object

smile.stat.Stat

public class Stat
extends java.lang.Object

Statistical functions or tests.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	Stat.chisq Chi-square test.
static class	Stat.cor Correlation test.
static class	Stat.F F-test.
static class	Stat.KS The Kolmogorov-Smirnov test (K-S test).
static class	Stat.t t-test.

Method Summary

Modifier and Type	Method and Description
static double	bic(double L, int v, int n) Bayesian information criterion (BIC).
static double	GoodTuring(int[] r, int[] Nr, double[] p) Good–Turing frequency estimation.

Methods inherited from class java.lang.Object

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

Method Detail

bic

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

Bayesian information criterion (BIC). 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.

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.

GoodTuring

public static double GoodTuring(int[] r,
                                int[] Nr,
                                double[] p)

Good–Turing frequency estimation. This technique is for estimating the probability of encountering an object of a hitherto unseen species, given a set of past observations of objects from different species. In drawing balls from an urn, the 'objects' would be balls and the 'species' would be the distinct colors of the balls (finite but unknown in number). After drawing R_red red balls, R_black black balls and , R_green green balls, we would ask what is the probability of drawing a red ball, a black ball, a green ball or one of a previously unseen color. This method takes a set of (frequency, frequency-of-frequency) pairs and estimate the probabilities corresponding to the observed frequencies, and P₀, the joint probability of all unobserved species.

Parameters:

r - the frequency in ascending order.

Nr - the frequency of frequencies.

p - on output, it is the estimated probabilities.

Returns:

P₀ for all unobserved species.