Examples with Gaussian org.apache.commons.math3.analysis.function.Gaussian used on opensource projects

Example 26 with Gaussian

use of org.apache.commons.math3.analysis.function.Gaussian in project gatk by broadinstitute.

the class GibbsSamplerSingleGaussianUnitTest method testRunMCMCOnSingleGaussianModel.

/**
     * Tests Bayesian inference of a Gaussian model via MCMC.  Recovery of input values for the variance and mean
     * global parameters is checked.  In particular, the mean and standard deviation of the posteriors for
     * both parameters must be recovered to within a relative error of 1% and 10%, respectively, in 250 samples
     * (after 250 burn-in samples have been discarded).
     */
@Test
public void testRunMCMCOnSingleGaussianModel() {
    //Create new instance of the Modeller helper class, passing all quantities needed to initialize state and data.
    final GaussianModeller modeller = new GaussianModeller(VARIANCE_INITIAL, MEAN_INITIAL, datapointsList);
    //Create a GibbsSampler, passing the total number of samples (including burn-in samples)
    //and the model held by the Modeller.
    final GibbsSampler<GaussianParameter, ParameterizedState<GaussianParameter>, GaussianDataCollection> gibbsSampler = new GibbsSampler<>(NUM_SAMPLES, modeller.model);
    //Run the MCMC.
    gibbsSampler.runMCMC();
    //Get the samples of each of the parameter posteriors (discarding burn-in samples) by passing the
    //parameter name, type, and burn-in number to the getSamples method.
    final double[] varianceSamples = Doubles.toArray(gibbsSampler.getSamples(GaussianParameter.VARIANCE, Double.class, NUM_BURN_IN));
    final double[] meanSamples = Doubles.toArray(gibbsSampler.getSamples(GaussianParameter.MEAN, Double.class, NUM_BURN_IN));
    //Check that the statistics---i.e., the means and standard deviations---of the posteriors
    //agree with those found by emcee/analytically to a relative error of 1% and 10%, respectively.
    final double variancePosteriorCenter = new Mean().evaluate(varianceSamples);
    final double variancePosteriorStandardDeviation = new StandardDeviation().evaluate(varianceSamples);
    Assert.assertEquals(relativeError(variancePosteriorCenter, VARIANCE_TRUTH), 0., RELATIVE_ERROR_THRESHOLD_FOR_CENTERS);
    Assert.assertEquals(relativeError(variancePosteriorStandardDeviation, VARIANCE_POSTERIOR_STANDARD_DEVIATION_TRUTH), 0., RELATIVE_ERROR_THRESHOLD_FOR_STANDARD_DEVIATIONS);
    final double meanPosteriorCenter = new Mean().evaluate(meanSamples);
    final double meanPosteriorStandardDeviation = new StandardDeviation().evaluate(meanSamples);
    Assert.assertEquals(relativeError(meanPosteriorCenter, MEAN_TRUTH), 0., RELATIVE_ERROR_THRESHOLD_FOR_CENTERS);
    Assert.assertEquals(relativeError(meanPosteriorStandardDeviation, MEAN_POSTERIOR_STANDARD_DEVIATION_TRUTH), 0., RELATIVE_ERROR_THRESHOLD_FOR_STANDARD_DEVIATIONS);
}

Example 27 with Gaussian

use of org.apache.commons.math3.analysis.function.Gaussian in project gatk by broadinstitute.

the class CopyRatioModellerUnitTest method testRunMCMCOnCopyRatioSegmentedGenome.

/**
     * Tests Bayesian inference of the copy-ratio model via MCMC.
     * <p>
     *     Recovery of input values for the variance and outlier-probability global parameters is checked.
     *     In particular, the true input value of the variance must fall within
     *     {@link CopyRatioModellerUnitTest#MULTIPLES_OF_SD_THRESHOLD}
     *     standard deviations of the posterior mean and the standard deviation of the posterior must agree
     *     with the analytic value to within a relative error of
     *     {@link CopyRatioModellerUnitTest#RELATIVE_ERROR_THRESHOLD} for 250 samples
     *     (after 250 burn-in samples have been discarded).  Similar criteria are applied
     *     to the recovery of the true input value for the outlier probability.
     * </p>
     * <p>
     *     Furthermore, the number of truth values for the segment-level means falling outside confidence intervals of
     *     1-sigma, 2-sigma, and 3-sigma given by the posteriors in each segment should be roughly consistent with
     *     a normal distribution (i.e., ~32, ~5, and ~0, respectively; we allow for errors of
     *     {@link CopyRatioModellerUnitTest#DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_1_SIGMA},
     *     {@link CopyRatioModellerUnitTest#DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_2_SIGMA}, and
     *     {@link CopyRatioModellerUnitTest#DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_3_SIGMA}, respectively).
     *     The mean of the standard deviations of the posteriors for the segment-level means should also be
     *     recovered to within a relative error of {@link CopyRatioModellerUnitTest#RELATIVE_ERROR_THRESHOLD}.
     * </p>
     * <p>
     *     Finally, the recovered values for the latent outlier-indicator parameters should agree with those used to
     *     generate the data.  For each indicator, the recovered value (i.e., outlier or non-outlier) is taken to be
     *     that given by the majority of posterior samples.  We require that at least
     *     {@link CopyRatioModellerUnitTest#FRACTION_OF_OUTLIER_INDICATORS_CORRECT_THRESHOLD}
     *     of the 10000 indicators are recovered correctly.
     * </p>
     * <p>
     *     With these specifications, this unit test is not overly brittle (i.e., it should pass for a large majority
     *     of randomly generated data sets), but it is still brittle enough to check for correctness of the sampling
     *     (for example, specifying a sufficiently incorrect likelihood will cause the test to fail).
     * </p>
     */
@Test
public void testRunMCMCOnCopyRatioSegmentedGenome() throws IOException {
    final JavaSparkContext ctx = SparkContextFactory.getTestSparkContext();
    LoggingUtils.setLoggingLevel(Log.LogLevel.INFO);
    //load data (coverages and number of targets in each segment)
    final ReadCountCollection coverage = ReadCountCollectionUtils.parse(COVERAGES_FILE);
    //Genome with no SNPs
    final Genome genome = new Genome(coverage, Collections.emptyList());
    final SegmentedGenome segmentedGenome = new SegmentedGenome(SEGMENT_FILE, genome);
    //run MCMC
    final CopyRatioModeller modeller = new CopyRatioModeller(segmentedGenome);
    modeller.fitMCMC(NUM_SAMPLES, NUM_BURN_IN);
    //check statistics of global-parameter posterior samples (i.e., posterior mode and standard deviation)
    final Map<CopyRatioParameter, PosteriorSummary> globalParameterPosteriorSummaries = modeller.getGlobalParameterPosteriorSummaries(CREDIBLE_INTERVAL_ALPHA, ctx);
    final PosteriorSummary variancePosteriorSummary = globalParameterPosteriorSummaries.get(CopyRatioParameter.VARIANCE);
    final double variancePosteriorCenter = variancePosteriorSummary.getCenter();
    final double variancePosteriorStandardDeviation = (variancePosteriorSummary.getUpper() - variancePosteriorSummary.getLower()) / 2;
    Assert.assertEquals(Math.abs(variancePosteriorCenter - VARIANCE_TRUTH), 0., MULTIPLES_OF_SD_THRESHOLD * VARIANCE_POSTERIOR_STANDARD_DEVIATION_TRUTH);
    Assert.assertEquals(relativeError(variancePosteriorStandardDeviation, VARIANCE_POSTERIOR_STANDARD_DEVIATION_TRUTH), 0., RELATIVE_ERROR_THRESHOLD);
    final PosteriorSummary outlierProbabilityPosteriorSummary = globalParameterPosteriorSummaries.get(CopyRatioParameter.OUTLIER_PROBABILITY);
    final double outlierProbabilityPosteriorCenter = outlierProbabilityPosteriorSummary.getCenter();
    final double outlierProbabilityPosteriorStandardDeviation = (outlierProbabilityPosteriorSummary.getUpper() - outlierProbabilityPosteriorSummary.getLower()) / 2;
    Assert.assertEquals(Math.abs(outlierProbabilityPosteriorCenter - OUTLIER_PROBABILITY_TRUTH), 0., MULTIPLES_OF_SD_THRESHOLD * OUTLIER_PROBABILITY_POSTERIOR_STANDARD_DEVIATION_TRUTH);
    Assert.assertEquals(relativeError(outlierProbabilityPosteriorStandardDeviation, OUTLIER_PROBABILITY_POSTERIOR_STANDARD_DEVIATION_TRUTH), 0., RELATIVE_ERROR_THRESHOLD);
    //check statistics of segment-mean posterior samples (i.e., posterior means and standard deviations)
    final List<Double> meansTruth = loadList(MEANS_TRUTH_FILE, Double::parseDouble);
    int numMeansOutsideOneSigma = 0;
    int numMeansOutsideTwoSigma = 0;
    int numMeansOutsideThreeSigma = 0;
    final int numSegments = meansTruth.size();
    //segment-mean posteriors are expected to be Gaussian, so PosteriorSummary for
    // {@link CopyRatioModellerUnitTest#CREDIBLE_INTERVAL_ALPHA}=0.32 is
    //(posterior mean, posterior mean - posterior standard devation, posterior mean + posterior standard deviation)
    final List<PosteriorSummary> meanPosteriorSummaries = modeller.getSegmentMeansPosteriorSummaries(CREDIBLE_INTERVAL_ALPHA, ctx);
    final double[] meanPosteriorStandardDeviations = new double[numSegments];
    for (int segment = 0; segment < numSegments; segment++) {
        final double meanPosteriorCenter = meanPosteriorSummaries.get(segment).getCenter();
        final double meanPosteriorStandardDeviation = (meanPosteriorSummaries.get(segment).getUpper() - meanPosteriorSummaries.get(segment).getLower()) / 2.;
        meanPosteriorStandardDeviations[segment] = meanPosteriorStandardDeviation;
        final double absoluteDifferenceFromTruth = Math.abs(meanPosteriorCenter - meansTruth.get(segment));
        if (absoluteDifferenceFromTruth > meanPosteriorStandardDeviation) {
            numMeansOutsideOneSigma++;
        }
        if (absoluteDifferenceFromTruth > 2 * meanPosteriorStandardDeviation) {
            numMeansOutsideTwoSigma++;
        }
        if (absoluteDifferenceFromTruth > 3 * meanPosteriorStandardDeviation) {
            numMeansOutsideThreeSigma++;
        }
    }
    final double meanPosteriorStandardDeviationsMean = new Mean().evaluate(meanPosteriorStandardDeviations);
    Assert.assertEquals(numMeansOutsideOneSigma, 100 - 68, DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_1_SIGMA);
    Assert.assertEquals(numMeansOutsideTwoSigma, 100 - 95, DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_2_SIGMA);
    Assert.assertTrue(numMeansOutsideThreeSigma <= DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_3_SIGMA);
    Assert.assertEquals(relativeError(meanPosteriorStandardDeviationsMean, MEAN_POSTERIOR_STANDARD_DEVIATION_MEAN_TRUTH), 0., RELATIVE_ERROR_THRESHOLD);
    //check accuracy of latent outlier-indicator posterior samples
    final List<CopyRatioState.OutlierIndicators> outlierIndicatorSamples = modeller.getOutlierIndicatorsSamples();
    int numIndicatorsCorrect = 0;
    final int numIndicatorSamples = outlierIndicatorSamples.size();
    final List<Integer> outlierIndicatorsTruthAsInt = loadList(OUTLIER_INDICATORS_TRUTH_FILE, Integer::parseInt);
    final List<Boolean> outlierIndicatorsTruth = outlierIndicatorsTruthAsInt.stream().map(i -> i == 1).collect(Collectors.toList());
    for (int target = 0; target < coverage.targets().size(); target++) {
        int numSamplesOutliers = 0;
        for (final CopyRatioState.OutlierIndicators sample : outlierIndicatorSamples) {
            if (sample.get(target)) {
                numSamplesOutliers++;
            }
        }
        //take predicted state of indicator to be given by the majority of samples
        if ((numSamplesOutliers >= numIndicatorSamples / 2.) == outlierIndicatorsTruth.get(target)) {
            numIndicatorsCorrect++;
        }
    }
    final double fractionOfOutlierIndicatorsCorrect = (double) numIndicatorsCorrect / coverage.targets().size();
    Assert.assertTrue(fractionOfOutlierIndicatorsCorrect >= FRACTION_OF_OUTLIER_INDICATORS_CORRECT_THRESHOLD);
}

Example 28 with Gaussian

use of org.apache.commons.math3.analysis.function.Gaussian in project gatk-protected by broadinstitute.

the class CopyRatioModellerUnitTest method testRunMCMCOnCopyRatioSegmentedGenome.

/**
     * Tests Bayesian inference of the copy-ratio model via MCMC.
     * <p>
     *     Recovery of input values for the variance and outlier-probability global parameters is checked.
     *     In particular, the true input value of the variance must fall within
     *     {@link CopyRatioModellerUnitTest#MULTIPLES_OF_SD_THRESHOLD}
     *     standard deviations of the posterior mean and the standard deviation of the posterior must agree
     *     with the analytic value to within a relative error of
     *     {@link CopyRatioModellerUnitTest#RELATIVE_ERROR_THRESHOLD} for 250 samples
     *     (after 250 burn-in samples have been discarded).  Similar criteria are applied
     *     to the recovery of the true input value for the outlier probability.
     * </p>
     * <p>
     *     Furthermore, the number of truth values for the segment-level means falling outside confidence intervals of
     *     1-sigma, 2-sigma, and 3-sigma given by the posteriors in each segment should be roughly consistent with
     *     a normal distribution (i.e., ~32, ~5, and ~0, respectively; we allow for errors of
     *     {@link CopyRatioModellerUnitTest#DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_1_SIGMA},
     *     {@link CopyRatioModellerUnitTest#DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_2_SIGMA}, and
     *     {@link CopyRatioModellerUnitTest#DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_3_SIGMA}, respectively).
     *     The mean of the standard deviations of the posteriors for the segment-level means should also be
     *     recovered to within a relative error of {@link CopyRatioModellerUnitTest#RELATIVE_ERROR_THRESHOLD}.
     * </p>
     * <p>
     *     Finally, the recovered values for the latent outlier-indicator parameters should agree with those used to
     *     generate the data.  For each indicator, the recovered value (i.e., outlier or non-outlier) is taken to be
     *     that given by the majority of posterior samples.  We require that at least
     *     {@link CopyRatioModellerUnitTest#FRACTION_OF_OUTLIER_INDICATORS_CORRECT_THRESHOLD}
     *     of the 10000 indicators are recovered correctly.
     * </p>
     * <p>
     *     With these specifications, this unit test is not overly brittle (i.e., it should pass for a large majority
     *     of randomly generated data sets), but it is still brittle enough to check for correctness of the sampling
     *     (for example, specifying a sufficiently incorrect likelihood will cause the test to fail).
     * </p>
     */
@Test
public void testRunMCMCOnCopyRatioSegmentedGenome() throws IOException {
    final JavaSparkContext ctx = SparkContextFactory.getTestSparkContext();
    LoggingUtils.setLoggingLevel(Log.LogLevel.INFO);
    //load data (coverages and number of targets in each segment)
    final ReadCountCollection coverage = ReadCountCollectionUtils.parse(COVERAGES_FILE);
    //Genome with no SNPs
    final Genome genome = new Genome(coverage, Collections.emptyList());
    final SegmentedGenome segmentedGenome = new SegmentedGenome(SEGMENT_FILE, genome);
    //run MCMC
    final CopyRatioModeller modeller = new CopyRatioModeller(segmentedGenome);
    modeller.fitMCMC(NUM_SAMPLES, NUM_BURN_IN);
    //check statistics of global-parameter posterior samples (i.e., posterior mode and standard deviation)
    final Map<CopyRatioParameter, PosteriorSummary> globalParameterPosteriorSummaries = modeller.getGlobalParameterPosteriorSummaries(CREDIBLE_INTERVAL_ALPHA, ctx);
    final PosteriorSummary variancePosteriorSummary = globalParameterPosteriorSummaries.get(CopyRatioParameter.VARIANCE);
    final double variancePosteriorCenter = variancePosteriorSummary.getCenter();
    final double variancePosteriorStandardDeviation = (variancePosteriorSummary.getUpper() - variancePosteriorSummary.getLower()) / 2;
    Assert.assertEquals(Math.abs(variancePosteriorCenter - VARIANCE_TRUTH), 0., MULTIPLES_OF_SD_THRESHOLD * VARIANCE_POSTERIOR_STANDARD_DEVIATION_TRUTH);
    Assert.assertEquals(relativeError(variancePosteriorStandardDeviation, VARIANCE_POSTERIOR_STANDARD_DEVIATION_TRUTH), 0., RELATIVE_ERROR_THRESHOLD);
    final PosteriorSummary outlierProbabilityPosteriorSummary = globalParameterPosteriorSummaries.get(CopyRatioParameter.OUTLIER_PROBABILITY);
    final double outlierProbabilityPosteriorCenter = outlierProbabilityPosteriorSummary.getCenter();
    final double outlierProbabilityPosteriorStandardDeviation = (outlierProbabilityPosteriorSummary.getUpper() - outlierProbabilityPosteriorSummary.getLower()) / 2;
    Assert.assertEquals(Math.abs(outlierProbabilityPosteriorCenter - OUTLIER_PROBABILITY_TRUTH), 0., MULTIPLES_OF_SD_THRESHOLD * OUTLIER_PROBABILITY_POSTERIOR_STANDARD_DEVIATION_TRUTH);
    Assert.assertEquals(relativeError(outlierProbabilityPosteriorStandardDeviation, OUTLIER_PROBABILITY_POSTERIOR_STANDARD_DEVIATION_TRUTH), 0., RELATIVE_ERROR_THRESHOLD);
    //check statistics of segment-mean posterior samples (i.e., posterior means and standard deviations)
    final List<Double> meansTruth = loadList(MEANS_TRUTH_FILE, Double::parseDouble);
    int numMeansOutsideOneSigma = 0;
    int numMeansOutsideTwoSigma = 0;
    int numMeansOutsideThreeSigma = 0;
    final int numSegments = meansTruth.size();
    //segment-mean posteriors are expected to be Gaussian, so PosteriorSummary for
    // {@link CopyRatioModellerUnitTest#CREDIBLE_INTERVAL_ALPHA}=0.32 is
    //(posterior mean, posterior mean - posterior standard devation, posterior mean + posterior standard deviation)
    final List<PosteriorSummary> meanPosteriorSummaries = modeller.getSegmentMeansPosteriorSummaries(CREDIBLE_INTERVAL_ALPHA, ctx);
    final double[] meanPosteriorStandardDeviations = new double[numSegments];
    for (int segment = 0; segment < numSegments; segment++) {
        final double meanPosteriorCenter = meanPosteriorSummaries.get(segment).getCenter();
        final double meanPosteriorStandardDeviation = (meanPosteriorSummaries.get(segment).getUpper() - meanPosteriorSummaries.get(segment).getLower()) / 2.;
        meanPosteriorStandardDeviations[segment] = meanPosteriorStandardDeviation;
        final double absoluteDifferenceFromTruth = Math.abs(meanPosteriorCenter - meansTruth.get(segment));
        if (absoluteDifferenceFromTruth > meanPosteriorStandardDeviation) {
            numMeansOutsideOneSigma++;
        }
        if (absoluteDifferenceFromTruth > 2 * meanPosteriorStandardDeviation) {
            numMeansOutsideTwoSigma++;
        }
        if (absoluteDifferenceFromTruth > 3 * meanPosteriorStandardDeviation) {
            numMeansOutsideThreeSigma++;
        }
    }
    final double meanPosteriorStandardDeviationsMean = new Mean().evaluate(meanPosteriorStandardDeviations);
    Assert.assertEquals(numMeansOutsideOneSigma, 100 - 68, DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_1_SIGMA);
    Assert.assertEquals(numMeansOutsideTwoSigma, 100 - 95, DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_2_SIGMA);
    Assert.assertTrue(numMeansOutsideThreeSigma <= DELTA_NUMBER_OF_MEANS_ALLOWED_OUTSIDE_3_SIGMA);
    Assert.assertEquals(relativeError(meanPosteriorStandardDeviationsMean, MEAN_POSTERIOR_STANDARD_DEVIATION_MEAN_TRUTH), 0., RELATIVE_ERROR_THRESHOLD);
    //check accuracy of latent outlier-indicator posterior samples
    final List<CopyRatioState.OutlierIndicators> outlierIndicatorSamples = modeller.getOutlierIndicatorsSamples();
    int numIndicatorsCorrect = 0;
    final int numIndicatorSamples = outlierIndicatorSamples.size();
    final List<Integer> outlierIndicatorsTruthAsInt = loadList(OUTLIER_INDICATORS_TRUTH_FILE, Integer::parseInt);
    final List<Boolean> outlierIndicatorsTruth = outlierIndicatorsTruthAsInt.stream().map(i -> i == 1).collect(Collectors.toList());
    for (int target = 0; target < coverage.targets().size(); target++) {
        int numSamplesOutliers = 0;
        for (final CopyRatioState.OutlierIndicators sample : outlierIndicatorSamples) {
            if (sample.get(target)) {
                numSamplesOutliers++;
            }
        }
        //take predicted state of indicator to be given by the majority of samples
        if ((numSamplesOutliers >= numIndicatorSamples / 2.) == outlierIndicatorsTruth.get(target)) {
            numIndicatorsCorrect++;
        }
    }
    final double fractionOfOutlierIndicatorsCorrect = (double) numIndicatorsCorrect / coverage.targets().size();
    Assert.assertTrue(fractionOfOutlierIndicatorsCorrect >= FRACTION_OF_OUTLIER_INDICATORS_CORRECT_THRESHOLD);
}

Example 29 with Gaussian

use of org.apache.commons.math3.analysis.function.Gaussian in project metron by apache.

the class OnlineStatisticsProviderTest method testNormallyDistributedRandomData.

@Test
public void testNormallyDistributedRandomData() {
    List<Double> values = new ArrayList<>();
    GaussianRandomGenerator gaussian = new GaussianRandomGenerator(new MersenneTwister(0L));
    for (int i = 0; i < 1000000; ++i) {
        double d = gaussian.nextNormalizedDouble();
        values.add(d);
    }
    validateEquality(values);
}

Example 30 with Gaussian

use of org.apache.commons.math3.analysis.function.Gaussian in project metron by apache.

the class OnlineStatisticsProviderTest method testNormallyDistributedRandomDataAllNegative.

@Test
public void testNormallyDistributedRandomDataAllNegative() {
    List<Double> values = new ArrayList<>();
    GaussianRandomGenerator gaussian = new GaussianRandomGenerator(new MersenneTwister(0L));
    for (int i = 0; i < 1000000; ++i) {
        double d = -1 * gaussian.nextNormalizedDouble();
        values.add(d);
    }
    validateEquality(values);
}