Bayesian Extremes: Markov Chain Monte Carlo

This lecture discusses how Markov chain Monte Carlo (MCMC) and other stochastic computation algorithms have enabled Bayesian techniques to be applied to extreme value problems. The advantages include the ability to include additional information through an appropriate prior, ease of inference, and the development of predictive inference. The lecture covers topics such as Bayesian inference, setting up Markov chains for posterior density calculation, and the Metropolis-Hastings algorithm. It also explores the importance of proper prior information in increasing the precision of extremal analysis and the challenges in specifying uncertainty in Bayesian inference. The lecture concludes with a discussion on the use of graphs for data exploration, model-checking, and presenting conclusions.