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Mathematical and statistical methods
/*
* This file is part of the repicea-mathstats library.
*
* Copyright (C) 2021-24 His Majesty the King in Right of Canada
* Author: Mathieu Fortin, Canadian Forest Service
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 3 of the License, or (at your option) any later version.
*
* This library is distributed with the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied
* warranty of MERCHANTABILITY or FITNESS FOR A
* PARTICULAR PURPOSE. See the GNU Lesser General Public
* License for more details.
*
* Please see the license at http://www.gnu.org/copyleft/lesser.html.
*/
package repicea.stats.estimators.mcmc;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;
import repicea.math.Matrix;
import repicea.math.SymmetricMatrix;
import repicea.stats.distributions.ContinuousDistribution;
import repicea.stats.distributions.GaussianDistribution;
/**
* A class to handle prior distributions.
* @author Mathieu Fortin - November 2021
*/
public class MetropolisHastingsPriorHandler {
private final Map distributions;
private final Map randomEffectDistributions;
private final List randomEffectList;
private int nbElements;
/**
* Package constructor.
*/
MetropolisHastingsPriorHandler() {
distributions = new LinkedHashMap();
randomEffectDistributions = new HashMap();
randomEffectList = new ArrayList();
}
/**
* Provide a realization of the parameters (fixed and random).
* @return a Matrix instance
*/
Matrix getRandomRealization() {
Matrix realizedParameters = new Matrix(nbElements, 1);
for (ContinuousDistribution d : distributions.keySet()) {
updateRandomEffectVariance(d, realizedParameters);
Matrix thisR = d.getRandomRealization();
int index = distributions.get(d);
realizedParameters.setElements(turnIntIntoArray(index), thisR);
}
return realizedParameters;
}
/**
* Update the variance of the random effects on the fly.
* @param d a ContinuousDistribution instance that stands for the distribution of a particular random effect
* @param realizedParameters the realized parameters generated from one realization of the Metropolis-Hastings algorithm.
*/
private void updateRandomEffectVariance(ContinuousDistribution d, Matrix realizedParameters) {
if (randomEffectDistributions.containsKey(d)) { // it is a random effect. So we must update its variance
ContinuousDistribution stdPrior = randomEffectDistributions.get(d);
int index = distributions.get(stdPrior);
Matrix realizedRandomEffectVariance = realizedParameters.getSubMatrix(index, index, 0, 0).elementWisePower(2d); // power 2 because we are dealing with the standard deviation
((GaussianDistribution) d).setVariance(SymmetricMatrix.convertToSymmetricIfPossible(realizedRandomEffectVariance));
}
}
/**
* Return the log probability density of the parameters (only fixed) with respect to the priors.
* @param realizedParameters
* @return a double
*/
double getLogProbabilityDensity(Matrix realizedParameters) {
double logProb = 0;
for (ContinuousDistribution d : distributions.keySet()) {
if (!randomEffectDistributions.containsKey(d)) { // we do not consider the random effects in the probability density of the prior
int index = distributions.get(d);
double thisProb = d.getProbabilityDensity(realizedParameters.getSubMatrix(turnIntIntoArray(index), null));
if (thisProb == 0d) {
return Double.NEGATIVE_INFINITY;
}
logProb += Math.log(thisProb);
}
}
return logProb;
}
double getLogProbabilityDensityOfRandomEffects(Matrix realizedParameters) {
double logProb = 0;
for (int i = 0; i < randomEffectList.size(); i++) {
double thisProb = getProbabilityDensityOfThisRandomEffect(realizedParameters, i);
if (thisProb == 0d) {
return Double.NEGATIVE_INFINITY;
} else {
logProb += Math.log(thisProb);
}
}
return logProb;
}
private double getProbabilityDensityOfThisRandomEffect(Matrix realizedParameters, int i) {
if (randomEffectList.isEmpty()) {
return 1d; // no random effect then prob = 1
} else {
GaussianDistribution d = randomEffectList.get(i);
updateRandomEffectVariance(d, realizedParameters);
int index = distributions.get(d);
return d.getProbabilityDensity(realizedParameters.getSubMatrix(turnIntIntoArray(index), null));
}
}
private List turnIntIntoArray(int i) {
return Arrays.asList(new Integer[] {i});
}
/**
* Add a prior distribution for a fixed effect parameter.
* @param dist a ContinuousDistribution instance
* @param index the index of the parameter associated with this distribution
*/
public void addFixedEffectDistribution(ContinuousDistribution dist, int index) {
// List ind = Arrays.asList(indices);
distributions.put(dist, index);
// nbElements += ind.size();
nbElements++;
}
/**
* Add a prior distribution for a random effect standard deviation.
*
* When assuming the existence of a random effect, it is good practice to assume
* the standard deviation is uniformly distributed and not the variance (Gelman 2006).
* @param dist a GaussianDistribution instance that stands for the distribution of a particular random effect.
* @param stdPrior a ContinuousDistribution instance that stands for the prior distribution of the random effect standard deviation.
* @param index the index of the parameter associated with this random effect
* @see Gelman 2006
*/
public void addRandomEffectStandardDeviation(GaussianDistribution dist, ContinuousDistribution stdPrior, int index) {
addFixedEffectDistribution(dist, index);
randomEffectDistributions.put(dist, stdPrior);
randomEffectList.add(dist);
}
/**
* Check if any prior distribution has been set.
* @return true if there is NO prior distribution in the handler yet.
*/
public boolean isEmpty() {
return distributions.isEmpty();
}
/**
* Clear the prior distributions.
*/
public void clear() {
nbElements = 0;
distributions.clear();
randomEffectDistributions.clear();
randomEffectList.clear();
}
}