Skip to content

bivariate.md

Latest commit

 

History

History
61 lines (42 loc) · 3.1 KB

bivariate.md

File metadata and controls

61 lines (42 loc) · 3.1 KB
Raw

Bivariate Analysis

<- Previous: Composite Analysis | Back to Index | Next: Coincident Frequency ->

BivariateAnalysis fits a BivariateDistribution consisting of two univariate marginals and a copula. It is used for joint frequency, conditional frequency, and as the upstream input to coincident frequency analysis.

Public API

API Purpose
BivariateDistribution(IUnivariateModel, IUnivariateModel, CopulaType) Creates the joint model
BivariateDistribution.CreateCopula(...) Creates supported Numerics copulas
BivariateDistribution.DataLogLikelihood(...) Joint likelihood
BivariateDistribution.PointwiseDataLogLikelihood(...) WAIC/LOO-CV support
BivariateDistribution.GenerateRandomValues(...) Joint simulation
BivariateAnalysis(BivariateDistribution) Analysis workflow
BivariateAnalysis.BayesianAnalysis MCMC settings and results
BivariateAnalysis.AnalysisResults Joint-frequency uncertainty results
BivariateAnalysis.CreateFrequencyAnalysisResultsAsync() Reprocesses frequency outputs

Usage Pattern

using Numerics.Distributions;
using Numerics.Distributions.Copulas;
using RMC.BestFit;
using RMC.BestFit.Analyses;
using RMC.BestFit.Models;

var xData = new DataFrame { ExactSeries = new ExactSeries(new[] { 10.0, 12.0, 14.0, 16.0 }) };
var yData = new DataFrame { ExactSeries = new ExactSeries(new[] { 5.0, 7.0, 9.0, 11.0 }) };

var marginalX = new UnivariateDistribution(xData, UnivariateDistributionType.Normal);
var marginalY = new UnivariateDistribution(yData, UnivariateDistributionType.Gumbel);

var model = new BivariateDistribution(marginalX, marginalY, CopulaType.Normal);
var analysis = new BivariateAnalysis(model);

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

Relationship To Coincident Frequency

BivariateAnalysis estimates the joint probability model for variables X and Y. Coincident Frequency combines that fitted joint model with a response surface Z = f(X, Y).

Source-Verified Likelihood

BivariateDistribution.DataLogLikelihood(...) estimates only the copula parameters. The marginal distributions are supplied by the two IUnivariateModel inputs. In pseudo-likelihood mode, BestFit evaluates the copula log density directly on pseudo-uniform sample pairs. In inference-from-margins mode, it transforms each raw pair through the marginal CDFs and then evaluates the copula log density. Non-finite or exception-producing likelihood evaluations return double.NegativeInfinity.

PointwiseDataLogLikelihood(...) follows the same path one pair at a time for WAIC, LOO-CV, and influence diagnostics.

Implementation Sources

Primary source paths: src/RMC.BestFit/Models/BivariateDistribution/BivariateDistribution.cs, src/RMC.BestFit/Analyses/Bivariate/BivariateAnalysis.cs, and src/RMC.BestFit/Analyses/Bivariate/CoincidentFrequencyAnalysis.cs.

<- Previous: Composite Analysis | Back to Index | Next: Coincident Frequency ->