dev.nm.stat.random.variancereduction

Class ImportanceSampling

java.lang.Object

dev.nm.stat.random.variancereduction.ImportanceSampling

All Implemented Interfaces:

MeanEstimator

public class ImportanceSampling
extends Object
implements MeanEstimator

Importance sampling is a general technique for estimating properties of a particular distribution, while only having samples generated from a different distribution rather than the distribution of interest. Specifically, \[ E_F(h(s)) = \int h(s)f(s) ds = \int h(s)\frac{f(s)}{g(s)}g(s)ds = \int h(s)w(s)g(s)ds = E_G(h(s)w(s)) \]

See Also:

Wikipedia: Importance sampling

Constructor Summary

Constructors

Constructor and Description
ImportanceSampling(UnivariateRealFunction h, UnivariateRealFunction w, RandomNumberGenerator G) Uses importance sample to do Monte Carlo integration.

Method Summary

Modifier and Type	Method and Description
Estimator	estimate(int n) Gets an estimator.

Methods inherited from class java.lang.Object

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

Constructor Detail

ImportanceSampling

public ImportanceSampling(UnivariateRealFunction h,
                          UnivariateRealFunction w,
                          RandomNumberGenerator G)

Uses importance sample to do Monte Carlo integration.

Parameters:

h - the function to integrate

w - the weight function or the change of measure

G - a uniform random number generator

Method Detail

estimate

public Estimator estimate(int n)

Description copied from interface: MeanEstimator

Gets an estimator.

Specified by:

estimate in interface MeanEstimator

Parameters:

n - the number of samples to draw for the estimation

Returns:

an estimator