Examples with Likelihood dr.inference.model.Likelihood used on opensource projects

Example 11 with Likelihood

use of dr.inference.model.Likelihood in project beast-mcmc by beast-dev.

the class TreeLoggerParser method parseXMLParameters.

protected void parseXMLParameters(XMLObject xo) throws XMLParseException {
    // reset this every time...
    branchRates = null;
    tree = (Tree) xo.getChild(Tree.class);
    title = xo.getAttribute(TITLE, "");
    nexusFormat = xo.getAttribute(NEXUS_FORMAT, false);
    sortTranslationTable = xo.getAttribute(SORT_TRANSLATION_TABLE, true);
    boolean substitutions = xo.getAttribute(BRANCH_LENGTHS, "").equals(SUBSTITUTIONS);
    List<TreeAttributeProvider> taps = new ArrayList<TreeAttributeProvider>();
    List<TreeTraitProvider> ttps = new ArrayList<TreeTraitProvider>();
    // ttps2 are for TTPs that are not specified within a Trait element. These are only
    // included if not already added through a trait element to avoid duplication of
    // (in particular) the BranchRates which is required for substitution trees.
    List<TreeTraitProvider> ttps2 = new ArrayList<TreeTraitProvider>();
    for (int i = 0; i < xo.getChildCount(); i++) {
        Object cxo = xo.getChild(i);
        if (cxo instanceof Likelihood) {
            final Likelihood likelihood = (Likelihood) cxo;
            taps.add(new TreeAttributeProvider() {

                public String[] getTreeAttributeLabel() {
                    return new String[] { "lnP" };
                }

                public String[] getAttributeForTree(Tree tree) {
                    return new String[] { Double.toString(likelihood.getLogLikelihood()) };
                }
            });
        }
        if (cxo instanceof TreeAttributeProvider) {
            taps.add((TreeAttributeProvider) cxo);
        }
        if (cxo instanceof TreeTraitProvider) {
            if (xo.hasAttribute(FILTER_TRAITS)) {
                String[] matches = ((String) xo.getAttribute(FILTER_TRAITS)).split("[\\s,]+");
                TreeTraitProvider ttp = (TreeTraitProvider) cxo;
                TreeTrait[] traits = ttp.getTreeTraits();
                List<TreeTrait> filteredTraits = new ArrayList<TreeTrait>();
                for (String match : matches) {
                    for (TreeTrait trait : traits) {
                        if (trait.getTraitName().startsWith(match)) {
                            filteredTraits.add(trait);
                        }
                    }
                }
                if (filteredTraits.size() > 0) {
                    ttps2.add(new TreeTraitProvider.Helper(filteredTraits));
                }
            } else {
                // Add all of them
                ttps2.add((TreeTraitProvider) cxo);
            }
        }
        if (cxo instanceof XMLObject) {
            XMLObject xco = (XMLObject) cxo;
            if (xco.getName().equals(TREE_TRAIT)) {
                TreeTraitProvider ttp = (TreeTraitProvider) xco.getChild(TreeTraitProvider.class);
                if (xco.hasAttribute(NAME)) {
                    // a specific named trait is required (optionally with a tag to name it in the tree file)
                    String name = xco.getStringAttribute(NAME);
                    final TreeTrait trait = ttp.getTreeTrait(name);
                    if (trait == null) {
                        String childName = "TreeTraitProvider";
                        if (ttp instanceof Likelihood) {
                            childName = ((Likelihood) ttp).prettyName();
                        } else if (ttp instanceof Model) {
                            childName = ((Model) ttp).getModelName();
                        }
                        throw new XMLParseException("Trait named, " + name + ", not found for " + childName);
                    }
                    final String tag;
                    if (xco.hasAttribute(TAG)) {
                        tag = xco.getStringAttribute(TAG);
                    } else {
                        tag = name;
                    }
                    ttps.add(new TreeTraitProvider.Helper(tag, new TreeTrait() {

                        public String getTraitName() {
                            return tag;
                        }

                        public Intent getIntent() {
                            return trait.getIntent();
                        }

                        public Class getTraitClass() {
                            return trait.getTraitClass();
                        }

                        public Object getTrait(Tree tree, NodeRef node) {
                            return trait.getTrait(tree, node);
                        }

                        public String getTraitString(Tree tree, NodeRef node) {
                            return trait.getTraitString(tree, node);
                        }

                        public boolean getLoggable() {
                            return trait.getLoggable();
                        }
                    }));
                } else if (xo.hasAttribute(FILTER_TRAITS)) {
                    // else a filter attribute is given to ask for all traits that starts with a specific
                    // string
                    String[] matches = ((String) xo.getAttribute(FILTER_TRAITS)).split("[\\s,]+");
                    TreeTrait[] traits = ttp.getTreeTraits();
                    List<TreeTrait> filteredTraits = new ArrayList<TreeTrait>();
                    for (String match : matches) {
                        for (TreeTrait trait : traits) {
                            if (trait.getTraitName().startsWith(match)) {
                                filteredTraits.add(trait);
                            }
                        }
                    }
                    if (filteredTraits.size() > 0) {
                        ttps.add(new TreeTraitProvider.Helper(filteredTraits));
                    }
                } else {
                    // neither named or filtered traits so just add them all
                    ttps.add(ttp);
                }
            }
        }
        // be able to put arbitrary statistics in as tree attributes
        if (cxo instanceof Loggable) {
            final Loggable loggable = (Loggable) cxo;
            taps.add(new TreeAttributeProvider() {

                public String[] getTreeAttributeLabel() {
                    String[] labels = new String[loggable.getColumns().length];
                    for (int i = 0; i < loggable.getColumns().length; i++) {
                        labels[i] = loggable.getColumns()[i].getLabel();
                    }
                    return labels;
                }

                public String[] getAttributeForTree(Tree tree) {
                    String[] values = new String[loggable.getColumns().length];
                    for (int i = 0; i < loggable.getColumns().length; i++) {
                        values[i] = loggable.getColumns()[i].getFormatted();
                    }
                    return values;
                }
            });
        }
    }
    // inclusion of the codon partitioned robust counting TTP...
    if (ttps2.size() > 0) {
        ttps.addAll(ttps2);
    }
    if (substitutions) {
        branchRates = (BranchRates) xo.getChild(BranchRates.class);
    }
    if (substitutions && branchRates == null) {
        throw new XMLParseException("To log trees in units of substitutions a BranchRateModel must be provided");
    }
    // logEvery of zero only displays at the end
    logEvery = xo.getAttribute(LOG_EVERY, 0);
    //        double normaliseMeanRateTo = xo.getAttribute(NORMALISE_MEAN_RATE_TO, Double.NaN);
    // decimal places
    final int dp = xo.getAttribute(DECIMAL_PLACES, -1);
    if (dp != -1) {
        format = NumberFormat.getNumberInstance(Locale.ENGLISH);
        format.setMaximumFractionDigits(dp);
    }
    final PrintWriter pw = getLogFile(xo, getParserName());
    formatter = new TabDelimitedFormatter(pw);
    treeAttributeProviders = new TreeAttributeProvider[taps.size()];
    taps.toArray(treeAttributeProviders);
    treeTraitProviders = new TreeTraitProvider[ttps.size()];
    ttps.toArray(treeTraitProviders);
    // I think the default should be to have names rather than numbers, thus the false default - AJD
    // I think the default should be numbers - using names results in larger files and end user never
    // sees the numbers anyway as any software loading the nexus files does the translation - JH
    mapNames = xo.getAttribute(MAP_NAMES, true);
    condition = logEvery == 0 ? (TreeLogger.LogUpon) xo.getChild(TreeLogger.LogUpon.class) : null;
}

Example 12 with Likelihood

use of dr.inference.model.Likelihood in project beast-mcmc by beast-dev.

the class CheckPointTreeModifier method incorporateAdditionalTaxa.

/**
     * Add the remaining taxa, which can be identified through the TreeDataLikelihood XML elements.
     */
public ArrayList<NodeRef> incorporateAdditionalTaxa(CheckPointUpdaterApp.UpdateChoice choice, BranchRates rateModel) {
    System.out.println("Tree before adding taxa:\n" + treeModel.toString() + "\n");
    ArrayList<NodeRef> newTaxaNodes = new ArrayList<NodeRef>();
    for (String str : newTaxaNames) {
        for (int i = 0; i < treeModel.getExternalNodeCount(); i++) {
            if (treeModel.getNodeTaxon(treeModel.getExternalNode(i)).getId().equals(str)) {
                newTaxaNodes.add(treeModel.getExternalNode(i));
                //always take into account Taxon dates vs. dates set through a TreeModel
                System.out.println(treeModel.getNodeTaxon(treeModel.getExternalNode(i)).getId() + " with height " + treeModel.getNodeHeight(treeModel.getExternalNode(i)) + " or " + treeModel.getNodeTaxon(treeModel.getExternalNode(i)).getHeight());
            }
        }
    }
    System.out.println("newTaxaNodes length = " + newTaxaNodes.size());
    ArrayList<Taxon> currentTaxa = new ArrayList<Taxon>();
    for (int i = 0; i < treeModel.getExternalNodeCount(); i++) {
        boolean taxonFound = false;
        for (String str : newTaxaNames) {
            if (str.equals((treeModel.getNodeTaxon(treeModel.getExternalNode(i))).getId())) {
                taxonFound = true;
            }
        }
        if (!taxonFound) {
            System.out.println("Adding " + treeModel.getNodeTaxon(treeModel.getExternalNode(i)).getId() + " to list of current taxa");
            currentTaxa.add(treeModel.getNodeTaxon(treeModel.getExternalNode(i)));
        }
    }
    System.out.println("Current taxa count = " + currentTaxa.size());
    //iterate over both current taxa and to be added taxa
    boolean originTaxon = true;
    for (Taxon taxon : currentTaxa) {
        if (taxon.getHeight() == 0.0) {
            originTaxon = false;
            System.out.println("Current taxon " + taxon.getId() + " has node height 0.0");
        }
    }
    for (NodeRef newTaxon : newTaxaNodes) {
        if (treeModel.getNodeTaxon(newTaxon).getHeight() == 0.0) {
            originTaxon = false;
            System.out.println("New taxon " + treeModel.getNodeTaxon(newTaxon).getId() + " has node height 0.0");
        }
    }
    //check the Tree(Data)Likelihoods in the connected set of likelihoods
    //focus on TreeDataLikelihood, which has getTree() to get the tree for each likelihood
    //also get the DataLikelihoodDelegate from TreeDataLikelihood
    ArrayList<TreeDataLikelihood> likelihoods = new ArrayList<TreeDataLikelihood>();
    ArrayList<Tree> trees = new ArrayList<Tree>();
    ArrayList<DataLikelihoodDelegate> delegates = new ArrayList<DataLikelihoodDelegate>();
    for (Likelihood likelihood : Likelihood.CONNECTED_LIKELIHOOD_SET) {
        if (likelihood instanceof TreeDataLikelihood) {
            likelihoods.add((TreeDataLikelihood) likelihood);
            trees.add(((TreeDataLikelihood) likelihood).getTree());
            delegates.add(((TreeDataLikelihood) likelihood).getDataLikelihoodDelegate());
        }
    }
    //suggested to go through TreeDataLikelihoodParser and give it an extra option to create a HashMap
    //keyed by the tree; am currently not overly fond of this approach
    ArrayList<PatternList> patternLists = new ArrayList<PatternList>();
    for (DataLikelihoodDelegate del : delegates) {
        if (del instanceof BeagleDataLikelihoodDelegate) {
            patternLists.add(((BeagleDataLikelihoodDelegate) del).getPatternList());
        } else if (del instanceof MultiPartitionDataLikelihoodDelegate) {
            MultiPartitionDataLikelihoodDelegate mpdld = (MultiPartitionDataLikelihoodDelegate) del;
            List<PatternList> list = mpdld.getPatternLists();
            for (PatternList pList : list) {
                patternLists.add(pList);
            }
        }
    }
    if (patternLists.size() == 0) {
        throw new RuntimeException("No patterns detected. Please make sure the XML file is BEAST 1.9 compatible.");
    }
    //aggregate all patterns to create distance matrix
    //TODO What about different trees for different partitions?
    Patterns patterns = new Patterns(patternLists.get(0));
    if (patternLists.size() > 1) {
        for (int i = 1; i < patternLists.size(); i++) {
            patterns.addPatterns(patternLists.get(i));
        }
    }
    //set the patterns for the distance matrix computations
    choice.setPatterns(patterns);
    //add new taxa one at a time
    System.out.println("Adding " + newTaxaNodes.size() + " taxa ...");
    for (NodeRef newTaxon : newTaxaNodes) {
        treeModel.setNodeHeight(newTaxon, treeModel.getNodeTaxon(newTaxon).getHeight());
        System.out.println("\nadding Taxon: " + newTaxon + " (height = " + treeModel.getNodeHeight(newTaxon) + ")");
        //check if this taxon has a more recent sampling date than all other nodes in the current TreeModel
        double offset = checkCurrentTreeNodes(newTaxon, treeModel.getRoot());
        System.out.println("Sampling date offset when adding " + newTaxon + " = " + offset);
        //AND set its current node height to 0.0 IF no originTaxon has been found
        if (offset < 0.0) {
            if (!originTaxon) {
                System.out.println("Updating all node heights with offset " + Math.abs(offset));
                updateAllTreeNodes(Math.abs(offset), treeModel.getRoot());
                treeModel.setNodeHeight(newTaxon, 0.0);
            }
        } else if (offset == 0.0) {
            if (!originTaxon) {
                treeModel.setNodeHeight(newTaxon, 0.0);
            }
        }
        //get the closest Taxon to the Taxon that needs to be added
        //take into account which taxa can currently be chosen
        Taxon closest = choice.getClosestTaxon(treeModel.getNodeTaxon(newTaxon), currentTaxa);
        System.out.println("\nclosest Taxon: " + closest + " with original height: " + closest.getHeight());
        //get the distance between these two taxa
        double distance = choice.getDistance(treeModel.getNodeTaxon(newTaxon), closest);
        System.out.println("at distance: " + distance);
        //TODO what if distance == 0.0 ??? how to choose closest taxon then (in absence of geo info)?
        //find the NodeRef for the closest Taxon (do not rely on node numbering)
        NodeRef closestRef = null;
        //careful with node numbering and subtract number of new taxa
        for (int i = 0; i < treeModel.getExternalNodeCount(); i++) {
            if (treeModel.getNodeTaxon(treeModel.getExternalNode(i)) == closest) {
                closestRef = treeModel.getExternalNode(i);
            }
        }
        System.out.println(closestRef + " with height " + treeModel.getNodeHeight(closestRef));
        //System.out.println("trying to set node height: " + closestRef + " from " + treeModel.getNodeHeight(closestRef) + " to " + closest.getHeight());
        //treeModel.setNodeHeight(closestRef, closest.getHeight());
        double timeForDistance = distance / rateModel.getBranchRate(treeModel, closestRef);
        System.out.println("timeForDistance = " + timeForDistance);
        //get parent node of branch that will be split
        NodeRef parent = treeModel.getParent(closestRef);
        //determine height of new node
        double insertHeight;
        if (treeModel.getNodeHeight(closestRef) == treeModel.getNodeHeight(newTaxon)) {
            insertHeight = treeModel.getNodeHeight(closestRef) + timeForDistance / 2.0;
            System.out.println("treeModel.getNodeHeight(closestRef) == treeModel.getNodeHeight(newTaxon): " + insertHeight);
            if (insertHeight >= treeModel.getNodeHeight(parent)) {
                insertHeight = treeModel.getNodeHeight(closestRef) + EPSILON * (treeModel.getNodeHeight(parent) - treeModel.getNodeHeight(closestRef));
            }
        } else {
            double remainder = (timeForDistance - Math.abs(treeModel.getNodeHeight(closestRef) - treeModel.getNodeHeight(newTaxon))) / 2.0;
            if (remainder > 0) {
                insertHeight = Math.max(treeModel.getNodeHeight(closestRef), treeModel.getNodeHeight(newTaxon)) + remainder;
                System.out.println("remainder > 0: " + insertHeight);
                if (insertHeight >= treeModel.getNodeHeight(parent)) {
                    insertHeight = treeModel.getNodeHeight(closestRef) + EPSILON * (treeModel.getNodeHeight(parent) - treeModel.getNodeHeight(closestRef));
                }
            } else {
                insertHeight = EPSILON * (treeModel.getNodeHeight(parent) - Math.max(treeModel.getNodeHeight(closestRef), treeModel.getNodeHeight(newTaxon)));
                insertHeight += Math.max(treeModel.getNodeHeight(closestRef), treeModel.getNodeHeight(newTaxon));
                System.out.println("remainder <= 0: " + insertHeight);
            }
        }
        System.out.println("insert at height: " + insertHeight);
        //pass on all the necessary variables to a method that adds the new taxon to the tree
        addTaxonAlongBranch(newTaxon, parent, closestRef, insertHeight);
        //option to print tree after each taxon addition
        System.out.println("\nTree after adding taxon " + newTaxon + ":\n" + treeModel.toString());
        //add newly added Taxon to list of current taxa
        currentTaxa.add(treeModel.getNodeTaxon(newTaxon));
    }
    return newTaxaNodes;
}

Example 13 with Likelihood

use of dr.inference.model.Likelihood in project beast-mcmc by beast-dev.

the class FactorRJMCMCOperatorParser method parseXMLObject.

@Override
public Object parseXMLObject(XMLObject xo) throws XMLParseException {
    //attributes
    double weight = xo.getDoubleAttribute(WEIGHT);
    int chainLength = xo.getIntegerAttribute(CHAIN_LENGTH);
    double sizeParameter = xo.getDoubleAttribute(SIZE_PARAMETER);
    //declaration
    AdaptableSizeFastMatrixParameter factors, loadings, cutoffs, loadingsSparcity;
    //parameters
    if (xo.hasChildNamed(FACTORS))
        factors = (AdaptableSizeFastMatrixParameter) xo.getChild(FACTORS).getChild(AdaptableSizeFastMatrixParameter.class);
    else
        factors = null;
    loadings = (AdaptableSizeFastMatrixParameter) xo.getChild(LOADINGS).getChild(AdaptableSizeFastMatrixParameter.class);
    if (xo.hasChildNamed(CUTOFFS)) {
        cutoffs = (AdaptableSizeFastMatrixParameter) xo.getChild(CUTOFFS).getChild(AdaptableSizeFastMatrixParameter.class);
    } else
        cutoffs = null;
    if (xo.hasChildNamed(LOADINGS_SPARSITY))
        loadingsSparcity = (AdaptableSizeFastMatrixParameter) xo.getChild(LOADINGS_SPARSITY).getChild(AdaptableSizeFastMatrixParameter.class);
    else
        loadingsSparcity = null;
    //models
    DeterminentalPointProcessPrior DPP = null;
    if (xo.getChild(SPARSITY_PRIOR) != null)
        DPP = (DeterminentalPointProcessPrior) xo.getChild(SPARSITY_PRIOR).getChild(DeterminentalPointProcessPrior.class);
    SimpleMCMCOperator NOp = null;
    if (xo.getChild(NEGATION_OPERATOR) != null) {
        NOp = (SimpleMCMCOperator) xo.getChild(NEGATION_OPERATOR).getChild(SimpleMCMCOperator.class);
    }
    AbstractModelLikelihood LFM = (AbstractModelLikelihood) xo.getChild(AbstractModelLikelihood.class);
    RowDimensionPoissonPrior rowPrior = (RowDimensionPoissonPrior) xo.getChild(ROW_PRIOR).getChild(RowDimensionPoissonPrior.class);
    Likelihood loadingsPrior = null;
    if (xo.hasChildNamed(LOADINGS_PRIOR)) {
        loadingsPrior = (Likelihood) xo.getChild(LOADINGS_PRIOR).getChild(Likelihood.class);
    }
    //operators
    BitFlipOperator sparsityOperator = null;
    if (xo.getChild(BitFlipOperator.class) != null)
        sparsityOperator = (BitFlipOperator) xo.getChild(BitFlipOperator.class);
    SimpleMCMCOperator loadingsOperator = (SimpleMCMCOperator) xo.getChild(LOADINGS_OPERATOR).getChild(SimpleMCMCOperator.class);
    SimpleMCMCOperator factorOperator = null;
    if (xo.getChild(FACTOR_OPERATOR) != null)
        factorOperator = (SimpleMCMCOperator) xo.getChild(FACTOR_OPERATOR).getChild(FactorTreeGibbsOperator.class);
    return new FactorRJMCMCOperator(weight, sizeParameter, chainLength, factors, loadings, cutoffs, loadingsSparcity, LFM, DPP, loadingsPrior, loadingsOperator, factorOperator, sparsityOperator, NOp, rowPrior);
}

Example 14 with Likelihood

use of dr.inference.model.Likelihood in project beast-mcmc by beast-dev.

the class MLOptimizerParser method parseXMLObject.

public Object parseXMLObject(XMLObject xo) throws XMLParseException {
    int chainLength = xo.getIntegerAttribute(CHAIN_LENGTH);
    OperatorSchedule opsched = null;
    dr.inference.model.Likelihood likelihood = null;
    ArrayList<Logger> loggers = new ArrayList<Logger>();
    for (int i = 0; i < xo.getChildCount(); i++) {
        Object child = xo.getChild(i);
        if (child instanceof dr.inference.model.Likelihood) {
            likelihood = (dr.inference.model.Likelihood) child;
        } else if (child instanceof OperatorSchedule) {
            opsched = (OperatorSchedule) child;
        } else if (child instanceof Logger) {
            loggers.add((Logger) child);
        } else {
            throw new XMLParseException("Unrecognized element found in optimizer element:" + child);
        }
    }
    Logger[] loggerArray = new Logger[loggers.size()];
    loggers.toArray(loggerArray);
    return new MLOptimizer("optimizer1", chainLength, likelihood, opsched, loggerArray);
}

Example 15 with Likelihood

use of dr.inference.model.Likelihood in project beast-mcmc by beast-dev.

the class LognormalPriorTest method testLognormalPrior.

public void testLognormalPrior() {
    //        ConstantPopulation constant = new ConstantPopulation(Units.Type.YEARS);
    //        constant.setN0(popSize); // popSize
    Parameter popSize = new Parameter.Default(6.0);
    popSize.setId(ConstantPopulationModelParser.POPULATION_SIZE);
    ConstantPopulationModel demo = new ConstantPopulationModel(popSize, Units.Type.YEARS);
    //Likelihood
    Likelihood dummyLikelihood = new DummyLikelihood(demo);
    // Operators
    OperatorSchedule schedule = new SimpleOperatorSchedule();
    MCMCOperator operator = new ScaleOperator(popSize, 0.75);
    operator.setWeight(1.0);
    schedule.addOperator(operator);
    // Log
    ArrayLogFormatter formatter = new ArrayLogFormatter(false);
    MCLogger[] loggers = new MCLogger[2];
    loggers[0] = new MCLogger(formatter, 1000, false);
    //        loggers[0].add(treeLikelihood);
    loggers[0].add(popSize);
    loggers[1] = new MCLogger(new TabDelimitedFormatter(System.out), 100000, false);
    //        loggers[1].add(treeLikelihood);
    loggers[1].add(popSize);
    // MCMC
    MCMC mcmc = new MCMC("mcmc1");
    MCMCOptions options = new MCMCOptions(1000000);
    // meanInRealSpace="false"
    DistributionLikelihood logNormalLikelihood = new DistributionLikelihood(new LogNormalDistribution(1.0, 1.0), 0);
    logNormalLikelihood.addData(popSize);
    List<Likelihood> likelihoods = new ArrayList<Likelihood>();
    likelihoods.add(logNormalLikelihood);
    Likelihood prior = new CompoundLikelihood(0, likelihoods);
    likelihoods.clear();
    likelihoods.add(dummyLikelihood);
    Likelihood likelihood = new CompoundLikelihood(-1, likelihoods);
    likelihoods.clear();
    likelihoods.add(prior);
    likelihoods.add(likelihood);
    Likelihood posterior = new CompoundLikelihood(0, likelihoods);
    mcmc.setShowOperatorAnalysis(true);
    mcmc.init(options, posterior, schedule, loggers);
    mcmc.run();
    // time
    System.out.println(mcmc.getTimer().toString());
    // Tracer
    List<Trace> traces = formatter.getTraces();
    ArrayTraceList traceList = new ArrayTraceList("LognormalPriorTest", traces, 0);
    for (int i = 1; i < traces.size(); i++) {
        traceList.analyseTrace(i);
    }
    //      <expectation name="param" value="4.48168907"/>
    TraceCorrelation popSizeStats = traceList.getCorrelationStatistics(traceList.getTraceIndex(ConstantPopulationModelParser.POPULATION_SIZE));
    System.out.println("Expectation of Log-Normal(1,1) is e^(M+S^2/2) = e^(1.5) = " + Math.exp(1.5));
    assertExpectation(ConstantPopulationModelParser.POPULATION_SIZE, popSizeStats, Math.exp(1.5));
}