Examples with Precision org.apache.commons.math3.util.Precision used on opensource projects

Example 21 with Precision

use of org.apache.commons.math3.util.Precision in project GDSC-SMLM by aherbert.

the class PCPALMMolecules method calculateAveragePrecision.

/**
	 * Calculate the average precision by fitting a skewed Gaussian to the histogram of the precision distribution.
	 * <p>
	 * A simple mean and SD of the histogram is computed. If the mean of the Skewed Gaussian does not fit within 3 SDs
	 * of the simple mean then the simple mean is returned.
	 * 
	 * @param molecules
	 * @param title
	 *            the plot title (null if no plot should be displayed)
	 * @param histogramBins
	 * @param logFitParameters
	 *            Record the fit parameters to the ImageJ log
	 * @param removeOutliers
	 *            The distribution is created using all values within 1.5x the inter-quartile range (IQR) of the data
	 * @return The average precision
	 */
public double calculateAveragePrecision(ArrayList<Molecule> molecules, String title, int histogramBins, boolean logFitParameters, boolean removeOutliers) {
    // Plot histogram of the precision
    float[] data = new float[molecules.size()];
    DescriptiveStatistics stats = new DescriptiveStatistics();
    double yMin = Double.NEGATIVE_INFINITY, yMax = 0;
    for (int i = 0; i < data.length; i++) {
        data[i] = (float) molecules.get(i).precision;
        stats.addValue(data[i]);
    }
    // Set the min and max y-values using 1.5 x IQR 
    if (removeOutliers) {
        double lower = stats.getPercentile(25);
        double upper = stats.getPercentile(75);
        if (Double.isNaN(lower) || Double.isNaN(upper)) {
            if (logFitParameters)
                Utils.log("Error computing IQR: %f - %f", lower, upper);
        } else {
            double iqr = upper - lower;
            yMin = FastMath.max(lower - iqr, stats.getMin());
            yMax = FastMath.min(upper + iqr, stats.getMax());
            if (logFitParameters)
                Utils.log("  Data range: %f - %f. Plotting 1.5x IQR: %f - %f", stats.getMin(), stats.getMax(), yMin, yMax);
        }
    }
    if (yMin == Double.NEGATIVE_INFINITY) {
        yMin = stats.getMin();
        yMax = stats.getMax();
        if (logFitParameters)
            Utils.log("  Data range: %f - %f", yMin, yMax);
    }
    float[][] hist = Utils.calcHistogram(data, yMin, yMax, histogramBins);
    Plot2 plot = null;
    if (title != null) {
        plot = new Plot2(title, "Precision", "Frequency");
        float[] xValues = hist[0];
        float[] yValues = hist[1];
        if (xValues.length > 0) {
            double xPadding = 0.05 * (xValues[xValues.length - 1] - xValues[0]);
            plot.setLimits(xValues[0] - xPadding, xValues[xValues.length - 1] + xPadding, 0, Maths.max(yValues) * 1.05);
        }
        plot.addPoints(xValues, yValues, Plot2.BAR);
        Utils.display(title, plot);
    }
    // Extract non-zero data
    float[] x = Arrays.copyOf(hist[0], hist[0].length);
    float[] y = hist[1];
    int count = 0;
    float dx = (x[1] - x[0]) * 0.5f;
    for (int i = 0; i < y.length; i++) if (y[i] > 0) {
        x[count] = x[i] + dx;
        y[count] = y[i];
        count++;
    }
    x = Arrays.copyOf(x, count);
    y = Arrays.copyOf(y, count);
    // Sense check to fitted data. Get mean and SD of histogram
    double[] stats2 = Utils.getHistogramStatistics(x, y);
    double mean = stats2[0];
    if (logFitParameters)
        log("  Initial Statistics: %f +/- %f", stats2[0], stats2[1]);
    // Standard Gaussian fit
    double[] parameters = fitGaussian(x, y);
    if (parameters == null) {
        log("  Failed to fit initial Gaussian");
        return mean;
    }
    double newMean = parameters[1];
    double error = Math.abs(stats2[0] - newMean) / stats2[1];
    if (error > 3) {
        log("  Failed to fit Gaussian: %f standard deviations from histogram mean", error);
        return mean;
    }
    if (newMean < yMin || newMean > yMax) {
        log("  Failed to fit Gaussian: %f outside data range %f - %f", newMean, yMin, yMax);
        return mean;
    }
    mean = newMean;
    if (logFitParameters)
        log("  Initial Gaussian: %f @ %f +/- %f", parameters[0], parameters[1], parameters[2]);
    double[] initialSolution = new double[] { parameters[0], parameters[1], parameters[2], -1 };
    // Fit to a skewed Gaussian (or appropriate function)
    double[] skewParameters = fitSkewGaussian(x, y, initialSolution);
    if (skewParameters == null) {
        log("  Failed to fit Skewed Gaussian");
        return mean;
    }
    SkewNormalFunction sn = new SkewNormalFunction(skewParameters);
    if (logFitParameters)
        log("  Skewed Gaussian: %f @ %f +/- %f (a = %f) => %f +/- %f", skewParameters[0], skewParameters[1], skewParameters[2], skewParameters[3], sn.getMean(), Math.sqrt(sn.getVariance()));
    newMean = sn.getMean();
    error = Math.abs(stats2[0] - newMean) / stats2[1];
    if (error > 3) {
        log("  Failed to fit Skewed Gaussian: %f standard deviations from histogram mean", error);
        return mean;
    }
    if (newMean < yMin || newMean > yMax) {
        log("  Failed to fit Skewed Gaussian: %f outside data range %f - %f", newMean, yMin, yMax);
        return mean;
    }
    // Use original histogram x-axis to maintain all the bins
    if (plot != null) {
        x = hist[0];
        for (int i = 0; i < y.length; i++) x[i] += dx;
        plot.setColor(Color.red);
        addToPlot(plot, x, skewParameters, Plot2.LINE);
        plot.setColor(Color.black);
        Utils.display(title, plot);
    }
    // Return the average precision from the fitted curve
    return newMean;
}

Example 22 with Precision

use of org.apache.commons.math3.util.Precision in project GDSC-SMLM by aherbert.

the class SummariseResults method addSummary.

private void addSummary(StringBuilder sb, MemoryPeakResults result) {
    DescriptiveStatistics[] stats = new DescriptiveStatistics[2];
    char[] suffix = new char[2];
    for (int i = 0; i < stats.length; i++) {
        stats[i] = new DescriptiveStatistics();
        suffix[i] = 0;
    }
    if (result.hasNullResults()) {
        IJ.log("Null results in dataset: " + result.getName());
        if (removeNullResults == UNKNOWN) {
            GenericDialog gd = new GenericDialog(TITLE);
            gd.addMessage("There are invalid results in memory.\n \nClean these results?");
            gd.enableYesNoCancel();
            gd.hideCancelButton();
            gd.showDialog();
            removeNullResults = (gd.wasOKed()) ? YES : NO;
        }
        if (removeNullResults == NO)
            result = result.copy();
        result.removeNullResults();
    }
    final int size = result.size();
    if (size > 0) {
        // Check if we can use the stored precision
        if (result.hasStoredPrecision()) {
            suffix[0] = '*';
            for (PeakResult peakResult : result.getResults()) {
                stats[0].addValue(peakResult.getPrecision());
            }
        } else if (result.isCalibratedForPrecision()) {
            final double nmPerPixel = result.getNmPerPixel();
            final double gain = result.getGain();
            final boolean emCCD = result.isEMCCD();
            for (PeakResult peakResult : result.getResults()) {
                stats[0].addValue(peakResult.getPrecision(nmPerPixel, gain, emCCD));
            }
        }
        // SNR requires noise
        if (result.getHead().noise > 0) {
            for (PeakResult peakResult : result.getResults()) {
                stats[1].addValue(peakResult.getSignal() / peakResult.noise);
            }
        }
    }
    sb.append(result.getName());
    sb.append("\t").append(result.size());
    int maxT = getMaxT(result);
    sb.append("\t").append(maxT);
    final double exposureTime = (result.getCalibration() != null) ? result.getCalibration().getExposureTime() : 0;
    sb.append("\t").append(Utils.timeToString(maxT * exposureTime));
    if (size > 0) {
        boolean includeDeviations = result.getHead().paramsStdDev != null;
        long memorySize = MemoryPeakResults.estimateMemorySize(size, includeDeviations);
        String memory = MemoryPeakResults.memorySizeString(memorySize);
        sb.append("\t").append(memory);
    } else {
        sb.append("\t-");
    }
    Rectangle bounds = result.getBounds(true);
    sb.append(String.format("\t%d,%d,%d,%d\t%s\t%s\t%s", bounds.x, bounds.y, bounds.x + bounds.width, bounds.y + bounds.height, Utils.rounded(result.getNmPerPixel(), 4), Utils.rounded(result.getGain(), 4), Utils.rounded(exposureTime, 4)));
    for (int i = 0; i < stats.length; i++) {
        if (Double.isNaN(stats[i].getMean())) {
            sb.append("\t-\t-\t-\t-");
        } else {
            sb.append("\t").append(IJ.d2s(stats[i].getMean(), 3));
            if (suffix[i] != 0)
                sb.append(suffix[i]);
            sb.append("\t").append(IJ.d2s(stats[i].getPercentile(50), 3));
            sb.append("\t").append(IJ.d2s(stats[i].getMin(), 3));
            sb.append("\t").append(IJ.d2s(stats[i].getMax(), 3));
        }
    }
    sb.append("\n");
}

Example 23 with Precision

use of org.apache.commons.math3.util.Precision in project GDSC-SMLM by aherbert.

the class TraceDiffusion method saveTraceDistances.

private void saveTraceDistances(int nTraces, ArrayList<double[]> distances, StoredDataStatistics msdPerMolecule, StoredDataStatistics msdPerMoleculeAdjacent, StoredDataStatistics dStarPerMolecule, StoredDataStatistics dStarPerMoleculeAdjacent) {
    distancesFilename = Utils.getFilename("Trace_Distances_File", distancesFilename);
    if (distancesFilename != null) {
        distancesFilename = Utils.replaceExtension(distancesFilename, "xls");
        BufferedWriter out = null;
        try {
            FileOutputStream fos = new FileOutputStream(distancesFilename);
            out = new BufferedWriter(new OutputStreamWriter(fos, "UTF-8"));
            double[] msd = msdPerMolecule.getValues();
            double[] msd2 = msdPerMoleculeAdjacent.getValues();
            double[] dStar = dStarPerMolecule.getValues();
            double[] dStar2 = dStarPerMoleculeAdjacent.getValues();
            out.write(String.format("#%d traces : Precision = %s nm : Exposure time = %s s", nTraces, Utils.rounded(precision, 4), Utils.rounded(exposureTime, 4)));
            out.newLine();
            out.write(String.format("#TraceId\tMSD all-vs-all (um^2/s)\tMSD adjacent (um^2/s)\tD all-vs-all(um^2/s)\tD adjacent(um^2/s)\tDistances (um^2) per %ss ... ", Utils.rounded(exposureTime, 4)));
            out.newLine();
            for (int i = 0; i < msd.length; i++) {
                out.write(Integer.toString(i + 1));
                out.write('\t');
                out.write(Utils.rounded(msd[i], 4));
                out.write('\t');
                out.write(Utils.rounded(msd2[i], 4));
                out.write('\t');
                out.write(Utils.rounded(dStar[i], 4));
                out.write('\t');
                out.write(Utils.rounded(dStar2[i], 4));
                for (double d : distances.get(i)) {
                    out.write('\t');
                    out.write(Utils.rounded(d, 4));
                }
                out.newLine();
            }
        } catch (Exception e) {
        } finally {
            if (out != null) {
                try {
                    out.close();
                } catch (IOException e) {
                }
            }
        }
    }
}

Example 24 with Precision

use of org.apache.commons.math3.util.Precision in project GDSC-SMLM by aherbert.

the class FIRE method runQEstimation.

private void runQEstimation() {
    IJ.showStatus(TITLE + " ...");
    if (!showQEstimationInputDialog())
        return;
    MemoryPeakResults results = ResultsManager.loadInputResults(inputOption, false);
    if (results == null || results.size() == 0) {
        IJ.error(TITLE, "No results could be loaded");
        return;
    }
    if (results.getCalibration() == null) {
        IJ.error(TITLE, "The results are not calibrated");
        return;
    }
    results = cropToRoi(results);
    if (results.size() < 2) {
        IJ.error(TITLE, "No results within the crop region");
        return;
    }
    initialise(results, null);
    // We need localisation precision.
    // Build a histogram of the localisation precision.
    // Get the initial mean and SD and plot as a Gaussian.
    PrecisionHistogram histogram = calculatePrecisionHistogram();
    if (histogram == null) {
        IJ.error(TITLE, "No localisation precision available.\n \nPlease choose " + PrecisionMethod.FIXED + " and enter a precision mean and SD.");
        return;
    }
    StoredDataStatistics precision = histogram.precision;
    //String name = results.getName();
    double fourierImageScale = SCALE_VALUES[imageScaleIndex];
    int imageSize = IMAGE_SIZE_VALUES[imageSizeIndex];
    // Create the image and compute the numerator of FRC. 
    // Do not use the signal so results.size() is the number of localisations.
    IJ.showStatus("Computing FRC curve ...");
    FireImages images = createImages(fourierImageScale, imageSize, false);
    // DEBUGGING - Save the two images to disk. Load the images into the Matlab 
    // code that calculates the Q-estimation and make this plugin match the functionality.
    //IJ.save(new ImagePlus("i1", images.ip1), "/scratch/i1.tif");
    //IJ.save(new ImagePlus("i2", images.ip2), "/scratch/i2.tif");
    FRC frc = new FRC();
    frc.progress = progress;
    frc.setFourierMethod(fourierMethod);
    frc.setSamplingMethod(samplingMethod);
    frc.setPerimeterSamplingFactor(perimeterSamplingFactor);
    FRCCurve frcCurve = frc.calculateFrcCurve(images.ip1, images.ip2, images.nmPerPixel);
    if (frcCurve == null) {
        IJ.error(TITLE, "Failed to compute FRC curve");
        return;
    }
    IJ.showStatus("Running Q-estimation ...");
    // Note:
    // The method implemented here is based on Matlab code provided by Bernd Rieger.
    // The idea is to compute the spurious correlation component of the FRC Numerator
    // using an initial estimate of distribution of the localisation precision (assumed 
    // to be Gaussian). This component is the contribution of repeat localisations of 
    // the same molecule to the numerator and is modelled as an exponential decay
    // (exp_decay). The component is scaled by the Q-value which
    // is the average number of times a molecule is seen in addition to the first time.
    // At large spatial frequencies the scaled component should match the numerator,
    // i.e. at high resolution (low FIRE number) the numerator is made up of repeat 
    // localisations of the same molecule and not actual structure in the image.
    // The best fit is where the numerator equals the scaled component, i.e. num / (q*exp_decay) == 1.
    // The FRC Numerator is plotted and Q can be determined by
    // adjusting Q and the precision mean and SD to maximise the cost function.
    // This can be done interactively by the user with the effect on the FRC curve
    // dynamically updated and displayed.
    // Compute the scaled FRC numerator
    double qNorm = (1 / frcCurve.mean1 + 1 / frcCurve.mean2);
    double[] frcnum = new double[frcCurve.getSize()];
    for (int i = 0; i < frcnum.length; i++) {
        FRCCurveResult r = frcCurve.get(i);
        frcnum[i] = qNorm * r.getNumerator() / r.getNumberOfSamples();
    }
    // Compute the spatial frequency and the region for curve fitting
    double[] q = FRC.computeQ(frcCurve, false);
    int low = 0, high = q.length;
    while (high > 0 && q[high - 1] > maxQ) high--;
    while (low < q.length && q[low] < minQ) low++;
    // Require we fit at least 10% of the curve
    if (high - low < q.length * 0.1) {
        IJ.error(TITLE, "Not enough points for Q estimation");
        return;
    }
    // Obtain initial estimate of Q plateau height and decay.
    // This can be done by fitting the precision histogram and then fixing the mean and sigma.
    // Or it can be done by allowing the precision to be sampled and the mean and sigma
    // become parameters for fitting.
    // Check if we can sample precision values
    boolean sampleDecay = precision != null && FIRE.sampleDecay;
    double[] exp_decay;
    if (sampleDecay) {
        // Random sample of precision values from the distribution is used to 
        // construct the decay curve
        int[] sample = Random.sample(10000, precision.getN(), new Well19937c());
        final double four_pi2 = 4 * Math.PI * Math.PI;
        double[] pre = new double[q.length];
        for (int i = 1; i < q.length; i++) pre[i] = -four_pi2 * q[i] * q[i];
        // Sample
        final int n = sample.length;
        double[] hq = new double[n];
        for (int j = 0; j < n; j++) {
            // Scale to SR pixels
            double s2 = precision.getValue(sample[j]) / images.nmPerPixel;
            s2 *= s2;
            for (int i = 1; i < q.length; i++) hq[i] += FastMath.exp(pre[i] * s2);
        }
        for (int i = 1; i < q.length; i++) hq[i] /= n;
        exp_decay = new double[q.length];
        exp_decay[0] = 1;
        for (int i = 1; i < q.length; i++) {
            double sinc_q = sinc(Math.PI * q[i]);
            exp_decay[i] = sinc_q * sinc_q * hq[i];
        }
    } else {
        // Note: The sigma mean and std should be in the units of super-resolution 
        // pixels so scale to SR pixels
        exp_decay = computeExpDecay(histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, q);
    }
    // Smoothing
    double[] smooth;
    if (loessSmoothing) {
        // Note: This computes the log then smooths it 
        double bandwidth = 0.1;
        int robustness = 0;
        double[] l = new double[exp_decay.length];
        for (int i = 0; i < l.length; i++) {
            // Original Matlab code computes the log for each array.
            // This is equivalent to a single log on the fraction of the two.
            // Perhaps the two log method is more numerically stable.
            //l[i] = Math.log(Math.abs(frcnum[i])) - Math.log(exp_decay[i]);
            l[i] = Math.log(Math.abs(frcnum[i] / exp_decay[i]));
        }
        try {
            LoessInterpolator loess = new LoessInterpolator(bandwidth, robustness);
            smooth = loess.smooth(q, l);
        } catch (Exception e) {
            IJ.error(TITLE, "LOESS smoothing failed");
            return;
        }
    } else {
        // Note: This smooths the curve before computing the log 
        double[] norm = new double[exp_decay.length];
        for (int i = 0; i < norm.length; i++) {
            norm[i] = frcnum[i] / exp_decay[i];
        }
        // Median window of 5 == radius of 2
        MedianWindow mw = new MedianWindow(norm, 2);
        smooth = new double[exp_decay.length];
        for (int i = 0; i < norm.length; i++) {
            smooth[i] = Math.log(Math.abs(mw.getMedian()));
            mw.increment();
        }
    }
    // Fit with quadratic to find the initial guess.
    // Note: example Matlab code frc_Qcorrection7.m identifies regions of the 
    // smoothed log curve with low derivative and only fits those. The fit is 
    // used for the final estimate. Fitting a subset with low derivative is not 
    // implemented here since the initial estimate is subsequently optimised 
    // to maximise a cost function. 
    Quadratic curve = new Quadratic();
    SimpleCurveFitter fit = SimpleCurveFitter.create(curve, new double[2]);
    WeightedObservedPoints points = new WeightedObservedPoints();
    for (int i = low; i < high; i++) points.add(q[i], smooth[i]);
    double[] estimate = fit.fit(points.toList());
    double qValue = FastMath.exp(estimate[0]);
    //System.out.printf("Initial q-estimate = %s => %.3f\n", Arrays.toString(estimate), qValue);
    // This could be made an option. Just use for debugging
    boolean debug = false;
    if (debug) {
        // Plot the initial fit and the fit curve
        double[] qScaled = FRC.computeQ(frcCurve, true);
        double[] line = new double[q.length];
        for (int i = 0; i < q.length; i++) line[i] = curve.value(q[i], estimate);
        String title = TITLE + " Initial fit";
        Plot2 plot = new Plot2(title, "Spatial Frequency (nm^-1)", "FRC Numerator");
        String label = String.format("Q = %.3f", qValue);
        plot.addPoints(qScaled, smooth, Plot.LINE);
        plot.setColor(Color.red);
        plot.addPoints(qScaled, line, Plot.LINE);
        plot.setColor(Color.black);
        plot.addLabel(0, 0, label);
        Utils.display(title, plot, Utils.NO_TO_FRONT);
    }
    if (fitPrecision) {
        // Q - Should this be optional?
        if (sampleDecay) {
            // If a sample of the precision was used to construct the data for the initial fit 
            // then update the estimate using the fit result since it will be a better start point. 
            histogram.sigma = precision.getStandardDeviation();
            // Normalise sum-of-squares to the SR pixel size
            double meanSumOfSquares = (precision.getSumOfSquares() / (images.nmPerPixel * images.nmPerPixel)) / precision.getN();
            histogram.mean = images.nmPerPixel * Math.sqrt(meanSumOfSquares - estimate[1] / (4 * Math.PI * Math.PI));
        }
        // Do a multivariate fit ...
        SimplexOptimizer opt = new SimplexOptimizer(1e-6, 1e-10);
        PointValuePair p = null;
        MultiPlateauness f = new MultiPlateauness(frcnum, q, low, high);
        double[] initial = new double[] { histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, qValue };
        p = findMin(p, opt, f, scale(initial, 0.1));
        p = findMin(p, opt, f, scale(initial, 0.5));
        p = findMin(p, opt, f, initial);
        p = findMin(p, opt, f, scale(initial, 2));
        p = findMin(p, opt, f, scale(initial, 10));
        if (p != null) {
            double[] point = p.getPointRef();
            histogram.mean = point[0] * images.nmPerPixel;
            histogram.sigma = point[1] * images.nmPerPixel;
            qValue = point[2];
        }
    } else {
        // If so then this should be optional.
        if (sampleDecay) {
            if (precisionMethod != PrecisionMethod.FIXED) {
                histogram.sigma = precision.getStandardDeviation();
                // Normalise sum-of-squares to the SR pixel size
                double meanSumOfSquares = (precision.getSumOfSquares() / (images.nmPerPixel * images.nmPerPixel)) / precision.getN();
                histogram.mean = images.nmPerPixel * Math.sqrt(meanSumOfSquares - estimate[1] / (4 * Math.PI * Math.PI));
            }
            exp_decay = computeExpDecay(histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, q);
        }
        // Estimate spurious component by promoting plateauness.
        // The Matlab code used random initial points for a Simplex optimiser.
        // A Brent line search should be pretty deterministic so do simple repeats.
        // However it will proceed downhill so if the initial point is wrong then 
        // it will find a sub-optimal result.
        UnivariateOptimizer o = new BrentOptimizer(1e-3, 1e-6);
        Plateauness f = new Plateauness(frcnum, exp_decay, low, high);
        UnivariatePointValuePair p = null;
        p = findMin(p, o, f, qValue, 0.1);
        p = findMin(p, o, f, qValue, 0.2);
        p = findMin(p, o, f, qValue, 0.333);
        p = findMin(p, o, f, qValue, 0.5);
        // Do some Simplex repeats as well
        SimplexOptimizer opt = new SimplexOptimizer(1e-6, 1e-10);
        p = findMin(p, opt, f, qValue * 0.1);
        p = findMin(p, opt, f, qValue * 0.5);
        p = findMin(p, opt, f, qValue);
        p = findMin(p, opt, f, qValue * 2);
        p = findMin(p, opt, f, qValue * 10);
        if (p != null)
            qValue = p.getPoint();
    }
    QPlot qplot = new QPlot(frcCurve, qValue, low, high);
    // Interactive dialog to estimate Q (blinking events per flourophore) using 
    // sliders for the mean and standard deviation of the localisation precision.
    showQEstimationDialog(histogram, qplot, frcCurve, images.nmPerPixel);
    IJ.showStatus(TITLE + " complete");
}

Example 25 with Precision

use of org.apache.commons.math3.util.Precision in project GDSC-SMLM by aherbert.

the class FIRE method calculatePrecisionHistogram.

/**
	 * Calculate a histogram of the precision. The precision can be either stored in the results or calculated using the
	 * Mortensen formula. If the precision method for Q estimation is not fixed then the histogram is fitted with a
	 * Gaussian to create an initial estimate.
	 *
	 * @param precisionMethod
	 *            the precision method
	 * @return The precision histogram
	 */
private PrecisionHistogram calculatePrecisionHistogram() {
    boolean logFitParameters = false;
    String title = results.getName() + " Precision Histogram";
    // Check if the results has the precision already or if it can be computed.
    boolean canUseStored = canUseStoredPrecision(results);
    boolean canCalculatePrecision = canCalculatePrecision(results);
    // Set the method to compute a histogram. Default to the user selected option.
    PrecisionMethod m = null;
    if (canUseStored && precisionMethod == PrecisionMethod.STORED)
        m = precisionMethod;
    else if (canCalculatePrecision && precisionMethod == PrecisionMethod.CALCULATE)
        m = precisionMethod;
    if (m == null) {
        // We only have two choices so if one is available then select it.
        if (canUseStored)
            m = PrecisionMethod.STORED;
        else if (canCalculatePrecision)
            m = PrecisionMethod.CALCULATE;
        // If the user selected a method not available then log a warning
        if (m != null && precisionMethod != PrecisionMethod.FIXED) {
            IJ.log(String.format("%s : Selected precision method '%s' not available, switching to '%s'", TITLE, precisionMethod, m.getName()));
        }
        if (m == null) {
            // This does not matter if the user has provide a fixed input.
            if (precisionMethod == PrecisionMethod.FIXED) {
                PrecisionHistogram histogram = new PrecisionHistogram(title);
                histogram.mean = mean;
                histogram.sigma = sigma;
                return histogram;
            }
            // No precision
            return null;
        }
    }
    // We get here if we can compute precision.
    // Build the histogram 
    StoredDataStatistics precision = new StoredDataStatistics(results.size());
    if (m == PrecisionMethod.STORED) {
        for (PeakResult r : results.getResults()) {
            precision.add(r.getPrecision());
        }
    } else {
        final double nmPerPixel = results.getNmPerPixel();
        final double gain = results.getGain();
        final boolean emCCD = results.isEMCCD();
        for (PeakResult r : results.getResults()) {
            precision.add(r.getPrecision(nmPerPixel, gain, emCCD));
        }
    }
    //System.out.printf("Raw p = %f\n", precision.getMean());
    double yMin = Double.NEGATIVE_INFINITY, yMax = 0;
    // Set the min and max y-values using 1.5 x IQR 
    DescriptiveStatistics stats = precision.getStatistics();
    double lower = stats.getPercentile(25);
    double upper = stats.getPercentile(75);
    if (Double.isNaN(lower) || Double.isNaN(upper)) {
        if (logFitParameters)
            Utils.log("Error computing IQR: %f - %f", lower, upper);
    } else {
        double iqr = upper - lower;
        yMin = FastMath.max(lower - iqr, stats.getMin());
        yMax = FastMath.min(upper + iqr, stats.getMax());
        if (logFitParameters)
            Utils.log("  Data range: %f - %f. Plotting 1.5x IQR: %f - %f", stats.getMin(), stats.getMax(), yMin, yMax);
    }
    if (yMin == Double.NEGATIVE_INFINITY) {
        int n = 5;
        yMin = Math.max(stats.getMin(), stats.getMean() - n * stats.getStandardDeviation());
        yMax = Math.min(stats.getMax(), stats.getMean() + n * stats.getStandardDeviation());
        if (logFitParameters)
            Utils.log("  Data range: %f - %f. Plotting mean +/- %dxSD: %f - %f", stats.getMin(), stats.getMax(), n, yMin, yMax);
    }
    // Get the data within the range
    double[] data = precision.getValues();
    precision = new StoredDataStatistics(data.length);
    for (double d : data) {
        if (d < yMin || d > yMax)
            continue;
        precision.add(d);
    }
    int histogramBins = Utils.getBins(precision, Utils.BinMethod.SCOTT);
    float[][] hist = Utils.calcHistogram(precision.getFloatValues(), yMin, yMax, histogramBins);
    PrecisionHistogram histogram = new PrecisionHistogram(hist, precision, title);
    if (precisionMethod == PrecisionMethod.FIXED) {
        histogram.mean = mean;
        histogram.sigma = sigma;
        return histogram;
    }
    // Fitting of the histogram to produce the initial estimate
    // Extract non-zero data
    float[] x = Arrays.copyOf(hist[0], hist[0].length);
    float[] y = hist[1];
    int count = 0;
    float dx = (x[1] - x[0]) * 0.5f;
    for (int i = 0; i < y.length; i++) if (y[i] > 0) {
        x[count] = x[i] + dx;
        y[count] = y[i];
        count++;
    }
    x = Arrays.copyOf(x, count);
    y = Arrays.copyOf(y, count);
    // Sense check to fitted data. Get mean and SD of histogram
    double[] stats2 = Utils.getHistogramStatistics(x, y);
    if (logFitParameters)
        Utils.log("  Initial Statistics: %f +/- %f", stats2[0], stats2[1]);
    histogram.mean = stats2[0];
    histogram.sigma = stats2[1];
    // Standard Gaussian fit
    double[] parameters = fitGaussian(x, y);
    if (parameters == null) {
        Utils.log("  Failed to fit initial Gaussian");
        return histogram;
    }
    double newMean = parameters[1];
    double error = Math.abs(stats2[0] - newMean) / stats2[1];
    if (error > 3) {
        Utils.log("  Failed to fit Gaussian: %f standard deviations from histogram mean", error);
        return histogram;
    }
    if (newMean < yMin || newMean > yMax) {
        Utils.log("  Failed to fit Gaussian: %f outside data range %f - %f", newMean, yMin, yMax);
        return histogram;
    }
    if (logFitParameters)
        Utils.log("  Initial Gaussian: %f @ %f +/- %f", parameters[0], parameters[1], parameters[2]);
    histogram.mean = parameters[1];
    histogram.sigma = parameters[2];
    return histogram;
}