Slice sampler and metropolis hastings approaches for bayesian analysis of extreme data - Rostami, Mohammad (2016)
Modelling the tails of distributions is important in many areas of research where the risk of unusually small or large events are of interest. In this research, application of extreme value theory within a Bayesian framework using the Metropolis Hastings algorithm and the slice sampler algorithm as an alternative approach, has been introduced. Selection of prior distributions are very crucial in Bayesian analysis. Here, we have exhaustedly studied all the possible priors for location and scale parameters and come out with a few suggestions for the prior selection of a Gumbel model. The slice sampler method can adaptively change the scale of changes made, which makes it easier to tune than Metropolis Hastings algorithm. Another important benefit of the slice sampler algorithm is that it provides posterior means with low errors for the shape parameters of the monthly maximum and threshold exceedances models. The slice sampler algorithm has been extended for more complex bivariate extreme value model with logistic dependence structure and exponential margins. A simulation study shows that the slice sampler algorithm provides posterior means with low errors for the parameters along with a high level of stationarity in iteration series. Furthermore, the slice sampler algorithm has been successfully applied to Malaysian gold returns which has been calculated using Malaysian daily gold prices from 2000 to 2011. By using a Bivariate extreme model and the slice sampler algorithm, the relationship between the gold and American dollar returns in Malaysian market has been considered.