# Multivariate Extremes: Bayesian Estimation of the Spectral Measure

## Help Pages

 BMAmevt-package Bayesian Model Averaging for Multivariate Extremes add.frame Adds graphical elements to a plot of the two dimensional simplex. BMAmevt Bayesian Model Averaging for Multivariate Extremes cons.angular.dat Angular data set generation from unit Frechet data. ddirimix Angular density/likelihood function in the Dirichlet Mixture model. ddirimix.grid Plots the Dirichlet mixture density on a discretization grid ddirimix.grid1D Univariate projection or marginalization of a Dirichlet mixture density on on '[0,1]' dgridplot Image and/or Contour plots of spectral densities in trivariate extreme value models diagnose Diagnostics for the MCMC output in the PB and NL models. diagnose.PBNLpostsample Diagnostics for the MCMC output in the PB and NL models. discretize Discretization grid builder. dm.expar.D3k3 Example of valid Dirichlet mixture parameter for tri-variate extremes. dnestlog Pairwise Beta (PB) and Nested Asymmetric Logistic (NL) distributions dnestlog.grid PB and NL spectral densities on the two-dimensional simplex dpairbeta Pairwise Beta (PB) and Nested Asymmetric Logistic (NL) distributions dpairbeta.grid PB and NL spectral densities on the two-dimensional simplex excessProb.condit.dm Probability of joint threshold exceedance, in the Dirichlet Mixture model, given a DM parameter. excessProb.condit.nl Probability of joint threshold excess in the NL model excessProb.nl Posterior distribution the probability of joint threshold excess, in the NL model. excessProb.pb Estimates the probability of joint excess (Frechet margins) expfunction.nl Exponent function in the NL model. frechetdat Multivariate data set with margins following unit Frechet distribution. invlogit Inverse logit transformation laplace.evt Laplace approximation of a model marginal likelihood by Laplace approximation. Leeds Tri-variate 'angular' data set approximately distributed according to a multivariate extremes angular distribution Leeds.frechet Multivariate data set with margins following unit Frechet distribution. logit Logit transformation marginal.lkl Marginal model likelihood marginal.lkl.nl Marginal likelihoods of the PB and NL models. marginal.lkl.pb Marginal likelihoods of the PB and NL models. maxLikelihood Maximum likelihood optimization MCpriorIntFun Generic Monte-Carlo integration of a function under the prior distribution MCpriorIntFun.nl Generic Monte-Carlo integration under the prior distribution in the PB and NL models. MCpriorIntFun.pb Generic Monte-Carlo integration under the prior distribution in the PB and NL models. nl.Hpar Default hyper-parameters for the NL model. nl.MCpar Default MCMC tuning parameter for the Nested Asymmetric logistic model. pb.Hpar Default hyper-parameters for the Pairwise Beta model. pb.MCpar Default MCMC tuning parameter for the Pairwise Beta model. posterior.predictive.nl Posterior predictive densities in the three dimensional PB, NL and NL3 models posterior.predictive.pb Posterior predictive densities in the three dimensional PB, NL and NL3 models posterior.predictive3D Posterior predictive density on the simplex, for three-dimensional extreme value models. posteriorDistr.bma Posterior distribution in the average model posteriorMCMC MCMC sampler for parametric spectral measures posteriorMCMC.nl MCMC posterior samplers for the pairwise beta and the negative logistic models. posteriorMCMC.pb MCMC posterior samplers for the pairwise beta and the negative logistic models. posteriorMean Posterior predictive density on the simplex, for three-dimensional extreme value models. posteriorWeights Posterior model weights prior.nl Prior parameter distribution for the NL model prior.pb Prior parameter distribution for the Pairwise Beta model proposal.nl NL3 model: proposal distribution. proposal.pb PB model: proposal distribution rdirichlet Dirichlet distribution: random generator rdirimix Angular density/likelihood function in the Dirichlet Mixture model. rect.integrate Density integration on the two-dimensional simplex rnestlog Pairwise Beta (PB) and Nested Asymmetric Logistic (NL) distributions rpairbeta Pairwise Beta (PB) and Nested Asymmetric Logistic (NL) distributions rstable.posit Positive alpha-stable distribution. scores3D Logarithmic score and L^2 distance between two densities on the simplex (trivariate case). transf.to.equi Linear coordinate transformations transf.to.rect Linear coordinate transformations winterdat Five-dimensional air quality dataset recorded in Leeds(U.K.), during five winter seasons.