composite.md

Composite Distributions

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Composite distributions combine multiple univariate analyses into a single distribution used for frequency results. BestFit exposes this through CompositeAnalysis, WeightedUnivariateAnalysis, CompositeType, and AverageMethod.

Composite Types

CompositeType	Meaning	Typical Use
CompetingRisks	Combines processes as a maximum or minimum	Rainfall vs. snowmelt annual maxima
Mixture	Weighted mixture of populations	Mixed flood populations
ModelAverage	Weighted average across candidate models	Model-form uncertainty

Model Averaging Methods

AverageMethod	Weight Source
AIC	Akaike Information Criterion from MLE fitting
BIC	Bayesian Information Criterion from MLE fitting
DIC	Bayesian deviance information criterion
WAIC	Watanabe-Akaike information criterion
LOOIC	PSIS leave-one-out information criterion
Equal	Equal component weights
RMSE	Plotting-position root mean square error

For AIC, BIC, DIC, WAIC, and LOOIC, CompositeAnalysis.EstimateModelWeights() gathers one criterion value from each successfully estimated child and passes the valid criterion vector to GoodnessOfFit.AICWeights(...). For RMSE, it calls GoodnessOfFit.RMSEWeights(...). For Equal, it assigns 1 / Analyses.Count to every child. Unestimated children receive zero weight and are not allowed through RunAsync(...).

Public API

Member	Purpose
CompositeAnalysis()	Creates an empty composite
CompositeAnalysis(IEnumerable<WeightedUnivariateAnalysis>)	Creates a composite from estimated child analyses
Analyses	Weighted child analyses
CompositeDistributionType	Selects competing risks, mixture, or model averaging
ModelAverageMethod	Selects the information criterion or weighting method
Dependency	Dependency assumption from Numerics probability helpers
IsMaximum	Max/min selection for competing risks
ProbabilityOrdinates	Output frequencies
BayesianAnalysis	Presentation and posterior-propagation settings

Usage Pattern

using RMC.BestFit.Analyses;

var components = new[]
{
    new WeightedUnivariateAnalysis(firstAnalysis, 0.50),
    new WeightedUnivariateAnalysis(secondAnalysis, 0.50)
};

var composite = new CompositeAnalysis(components)
{
    CompositeDistributionType = CompositeType.ModelAverage,
    ModelAverageMethod = AverageMethod.WAIC
};

if (composite.Validate().IsValid)
{
    await composite.RunAsync();
}

Constraints

WeightedUnivariateAnalysis rejects another CompositeAnalysis as a child. Composite-of-composite nesting is intentionally unsupported to avoid circular references and ambiguous weighting semantics.

For mixture and model-average output, BestFit constructs a Numerics.Distributions.Mixture from the child point-estimate or posterior-realization distributions. If the supplied weights sum to less than one, the resulting mixture is marked zero-inflated and the residual mass is stored in ZeroWeight. For competing risks, BestFit constructs Numerics.Distributions.CompetingRisks, passes through Dependency, and sets MinimumOfRandomVariables = !IsMaximum.

Implementation Sources

Primary source paths: src/RMC.BestFit/Analyses/Univariate/CompositeAnalysis.cs, src/RMC.BestFit/Analyses/Univariate/WeightedUnivariateAnalysis.cs, and src/RMC.BestFit/Analyses/Univariate/UncertaintyAnalysisResults.cs.

References

[1] K. P. Burnham and D. R. Anderson, Model Selection and Multimodel Inference, 2nd ed. New York, NY, USA: Springer, 2002.

[2] A. Vehtari, A. Gelman, and J. Gabry, "Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC," Statistics and Computing, vol. 27, no. 5, pp. 1413-1432, 2017.

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