A comprehensive study on the Bayesian modelling of extreme rainfall: A case study from Pakistan

In this paper, the modelling of extreme rainfall is carried out in Pakistan by analysing annual daily maximum rainfall data via frequentist and Bayesian approaches. In frequentist settings, the parameters and return levels of the best fitted probabilistic model (i.e., generalized extreme value) are estimated using maximum likelihood and linear moments method. On the other side, under the Bayesian framework, the parameters and return levels are calculated both for noninformative and informative priors. This task is completed with the help of the Markov Chain Monte Carlo method using the Metropolis‐Hasting algorithm. This study also highlights a procedure to build an informative prior through historical records of the underlying processes from other nearby weather stations. The findings attained from the Bayesian paradigm demonstrate that the posterior inference could be affected by the choice of past knowledge used for the construction of informative priors. Additionally, the best method for the modelling of extreme rainfall over the country is decided with the support of assessment measures. In general, the Bayesian paradigm linked with the informative priors offers an adequate estimations scheme in terms of accuracy as compared to frequentist methods, accounting for ambiguity in parameters and return levels. Hence, these findings are very helpful in adopting accurate flood protection measures and designing infrastructures over the country. The figure (a), (b), and (c) are the estimated densities of GEV parameters for the Hyderabad station of the province Sindh. Notice that the distributions of location parameter are symmetric and distributions of scale and shape parameters are looking positively skewed. The densities of location, scale, and shape parameters based on the informative priors have high peaks. The fluctuations in posterior densities indicate that the posterior distributions are sensitive to the informative priors.