gov.sandia.cognition.statistics.bayesian

Class BayesianUtil

java.lang.Object

gov.sandia.cognition.statistics.bayesian.BayesianUtil

public class BayesianUtil
extends java.lang.Object

Contains generally useful utilities for Bayesian statistics.

Since:

3.0

Author:

Kevin R. Dixon

Constructor Summary

Constructors

Constructor and Description
BayesianUtil()

Method Summary

Modifier and Type	Method and Description
static <ObservationType> double	deviance(ComputableDistribution<ObservationType> conditional, java.lang.Iterable<? extends ObservationType> observations) Computes the deviance of the model, which is -2log(p(observations|parameter)).
static <ObservationType,ParameterType> UnivariateGaussian	expectedDeviance(BayesianParameter<ParameterType,? extends ComputableDistribution<ObservationType>,?> predictiveDistribution, java.lang.Iterable<? extends ObservationType> observations, java.util.Random random, int numSamples) Computes the expected deviance of the model by sampling parameters from the posterior and then computing the deviance using the conditional distribution.
static UnivariateGaussian	getMean(java.util.Collection<? extends java.lang.Double> samples) Computes the Monte Carlo distribution of the given samples.
static <ObservationType> double	logLikelihood(ComputableDistribution<? super ObservationType> distribution, java.lang.Iterable<? extends ObservationType> observations) Computes the log likelihood of the i.i.d.
static <ObservationType,ParameterType> java.util.ArrayList<ObservationType>	sample(BayesianParameter<ParameterType,? extends Distribution<ObservationType>,? extends Distribution<ParameterType>> parameter, java.util.Random random, int numSamples) Samples from the given BayesianParameter by first sampling the prior distribution, then updating the conditional distribution, then sampling from the updated conditional distribution.
static <ObservationType,ParameterType> java.util.ArrayList<? extends ObservationType>	sample(ClosedFormDistribution<ObservationType> conditional, java.lang.String parameterName, Distribution<ParameterType> prior, java.util.Random random, int numSamples) Samples from the given BayesianParameter by first sampling the prior distribution, then updating the conditional distribution, then sampling from the updated conditional distribution.

Methods inherited from class java.lang.Object

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

Constructor Detail

BayesianUtil

public BayesianUtil()

Method Detail

logLikelihood

public static <ObservationType> double logLikelihood(ComputableDistribution<? super ObservationType> distribution,
                                                     java.lang.Iterable<? extends ObservationType> observations)

Computes the log likelihood of the i.i.d. data using the given probability function.

Type Parameters:

ObservationType - Type of observations to consider

Parameters:

distribution - Computable distribution from which to get the probability function (a pdf or pmf) used to compute the likelihood.

observations - Observations to compute the log likelihood of.

Returns:

Log likelihood of the i.i.d. data using the given probability function.

sample

public static <ObservationType,ParameterType> java.util.ArrayList<? extends ObservationType> sample(ClosedFormDistribution<ObservationType> conditional,
                                                                                                    java.lang.String parameterName,
                                                                                                    Distribution<ParameterType> prior,
                                                                                                    java.util.Random random,
                                                                                                    int numSamples)

Samples from the given BayesianParameter by first sampling the prior distribution, then updating the conditional distribution, then sampling from the updated conditional distribution.

Type Parameters:

ObservationType - Type of observations generated by the conditional distribution

ParameterType - Type of parameters generated by the prior distribution, used to update the conditional distribution

Parameters:

conditional - Conditional distribution that generates observations

parameterName - Name of the parameter in the conditional distribution that is generated according to the prior distribution

prior - Prior distribution of parameter values

random - Random number generator

numSamples - Number of samples to generate

Returns:

Samples from the given BayesianParameter by first sampling the prior distribution, then updating the conditional distribution, then sampling from the updated conditional distribution.

sample

public static <ObservationType,ParameterType> java.util.ArrayList<ObservationType> sample(BayesianParameter<ParameterType,? extends Distribution<ObservationType>,? extends Distribution<ParameterType>> parameter,
                                                                                          java.util.Random random,
                                                                                          int numSamples)

Samples from the given BayesianParameter by first sampling the prior distribution, then updating the conditional distribution, then sampling from the updated conditional distribution.

Type Parameters:

ObservationType - Type of observations generated by the conditional distribution

ParameterType - Type of parameters generated by the prior distribution, used to update the conditional distribution

Parameters:

parameter - BayesianParameter that links the conditional distribution via a parameter to a prior distribution.

random - Random number generator

numSamples - Number of samples to generate

Returns:

Samples from the given BayesianParameter by first sampling the prior distribution, then updating the conditional distribution, then sampling from the updated conditional distribution.

deviance

@PublicationReference(author={"Andrew Gelman","John B. Carlin","Hal S. Stern","Donald B. Rubin"},
                      title="Bayesian Data Analysis, Second Edition",
                      type=Book,
                      year=2004,
                      pages={180,181},
                      notes="Equation 6.6")
public static <ObservationType> double deviance(ComputableDistribution<ObservationType> conditional,
                                                                                                                                                                                                                                                                                                                                                                             java.lang.Iterable<? extends ObservationType> observations)

Computes the deviance of the model, which is -2log(p(observations|parameter)). This is proportional to the mean squared error if the model is normal with constant variance.

Type Parameters:

ObservationType -

Parameters:

conditional - Conditional distribution that generates observations.

observations - Observations to consider

Returns:

Deviance of the model.

expectedDeviance

@PublicationReference(author={"Andrew Gelman","John B. Carlin","Hal S. Stern","Donald B. Rubin"},
                      title="Bayesian Data Analysis, Second Edition",
                      type=Book,
                      year=2004,
                      pages={180,181},
                      notes="Equation 6.9")
public static <ObservationType,ParameterType> UnivariateGaussian expectedDeviance(BayesianParameter<ParameterType,? extends ComputableDistribution<ObservationType>,?> predictiveDistribution,
                                                                                                                                                                                                                                                                                                                                                                                                               java.lang.Iterable<? extends ObservationType> observations,
                                                                                                                                                                                                                                                                                                                                                                                                               java.util.Random random,
                                                                                                                                                                                                                                                                                                                                                                                                               int numSamples)

Computes the expected deviance of the model by sampling parameters from the posterior and then computing the deviance using the conditional distribution. This is also proportional to the Kullback-Leibler divergence of the posterior up to an additive constant. In the limit of infinite data, the model with the lowest expected deviance will have the highest posterior probability.

Type Parameters:

ObservationType - Type of observations generated by the conditional distribution.

ParameterType - Type of parameters generated by the posterior distribution.

Parameters:

predictiveDistribution - Relationship between the posterior (parameters) and the conditional (observations).

observations - Observations to consider when computing the deviance

random - Random number generator

numSamples - Number of samples to use in the expectation.

Returns:

Expected deviance of the model.

getMean

public static UnivariateGaussian getMean(java.util.Collection<? extends java.lang.Double> samples)

Computes the Monte Carlo distribution of the given samples.

Parameters:

samples - Samples to consider.

Returns:

Distribution describing the mean and estimated variance of the mean of the samples.