Fitting the Bartlett-Lewis Rainfall Model Using Approximate Bayesian Computation Event

12 October 2017
Building 16, Room 2025

For more information regarding this event, please email Huifu Xu at .

Event details

The Bartlett-Lewis rainfall model is a well-known model based on a clustered point process. It is defined using primary and secondary processes. The primary process is known as the parent process or the storm arrival process. Starting at each point of the parent process there is an associated secondary process called a daughter process or a cell arrival process. Each cell then has an associated rainfall duration and intensity, and the total rainfall intensity at time t is the sum of the intensities from all active cells at that time. The standard Bartlett-Lewis model uses a Poisson process for the storm arrival process. The cell arrival processes are also Poisson, stopped after an exponential time (the storm duration). Cell durations and intensities are also given independent exponential distributions. Even in its simplest form, this model has an intractable likelihood and cannot be fitted using maximum likelihood. Instead we consider two likelihood free parameter estimation regimes: Generalized Method of Moments (GMM) and Approximate Bayesian Computation (ABC). GMM is currently the preferred method for fitting Bartlett-Lewis rainfall models. This frequentist method compares empirical and theoretical statistics using weighted least squares. ABC is a new approach for fitting Poisson cluster rainfall models, and instead of the theoretical statistics used by GMM it uses simulated data statistics. This allows us to use statistics for which we have no nice theoretical expressions. ABC-MCMC combines ABC and Monte Carlo Markov Chain sampling. We present a comparative study of ABC Markov Chain Monte Carlo (ABC-MCMC) and GMM, using simulated and real data sets. We show that ABC-MCMC outperforms GMM when applied to Bartlett-Lewis rainfall models. This opens a new avenue for fitting Poisson cluster models to real data without having to derive theoretical statistics, which, in some cases, are impossible to obtain.

Speaker information

Owen Jones,Cardiff University ,OWEN JONES is an applied mathematician with a background in data analytics, optimisation and simulation. Many of his projects involve assembling data from divers sources, using it to build simulation models, then using those models to inform management decisions. Previous collaborators include the Australian Department of Agriculture, Fisheries and Forestry (planning for the Post Entry Quarantine facility, a national infrastructure project); the Australian Office of Transport Security (improving security procedures in Australian airports); Rate Valuation Services (a financial services company); McLaren International (the racing team); Merlin Power Systems (a feasibility study for an emergency response scheme for power generators in the UK); and National Air Traffic Systems (responsible for air traffic control in the UK). Prof. Jones' work makes use of a wide range of computational, analytical and mathematical techniques. He has taught graduate courses in machine learning and data mining, and he is the principal author of a best-selling text book on programming and simulation using the language R. Much of Prof. Jones' current research concerns complex spatio-temporal environmental data, in particular problems of water runoff in catchment areas.