This repository provides a framework to jointly model the bulk and tail data in a Bayesian approach.

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Simulation (Folder Simulation)

Main Code

Result_Analysis.R

• Code for diagnosing the goodness of fit in Scenario 1.1, 1.2, and 1.3 and comparing results from Scenario 2 with the model in André et al. (2024).

Auxiliaries

Run_Simulation_1.1.R
Run_Simulation_1.2.R
Run_Simulation_1.3.R

• Code for obtaining MCMC results of scenarios 1.1, 1.2, and 1.3 in the simulation section.

Run_Simulation_2.R

• Code for fitting the Bivariate Extreme Mixture Model on the Gaussian distributed data, referred to as Scenario 2 in the following. The result is compared with that in André et al. (2024).

BEMM_Functions.R
BEMM_Functions_AFSlice.R

• Nimble code for running MCMC on the Bivariate Extreme Mixture Model. The first uses a blocked random walk sampler, while the second uses the Automated Factor Sliced Sampler.

Posterior_Dependence.R

• Code for calculating chi, chi bar, and Kendall's tau of the posterior predictive replicate in Scenario 2.

plots.R

• Code for illustrating the Bivariate Extreme Mixture Model.

Functions.R
Lidia_model.R

• Code for reproducing results from André et al. (2024)

RevExp_U_Functions.r
CommonFunctions.r

• Code for fitting multivariate Generalized Pareto Distribution of a U representation and reverse exponential distribution as the generator. These two files are from the supporting material of Kiriliouk et al. (2019).

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Data Application (Folder UK_Temp)

Main Code

Temp_Result_Analysis.R

• Code for reproducing the analysis results.

Auxiliaries

east-sussex_oxfordshire.RData

• Data for analysis. The RData contains two data frames:
  1. temp.daily.max.all: raw daily maxixa air temperature data used in the analysis. column City 1 is the record from a station located in bishops lane, Ringmer, while column city 2 represents the record from a station located in Model Farm, Shirburn
  2. Y.all: residuals after removing the trend and periodic components.

East_sussex_Oxfordshire.R

• Code for fitting the Bivariate Extreme Mixture Model on the daily air temperature data.

BEMM_Function_Temp.R

• Nimble code for running the MCMC using the Automated Factor Sliced Sampler.

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Reference

André, L., Wadsworth, J. and O'Hagan, A. (2024) Joint modelling of the body and tail of bivariate data. Computational Statistics & Data Analysis 189, 107841.

Kiriliouk, A., Rootzén, H., Segers, J. and Wadsworth, J. L. (2019) Peaks over thresholds modeling with multivariate generalized Pareto distributions. Technometrics 61(1), 123–135.