Bayesian fitting procedures for hydrological point processes.
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Model fitting and selection typically requires the use of likelihoods. Applying standard methods to hydrological point processes, however, is problematic as their likelihoods are often analytically intractable and the data sets used for analysis are very large. We consider the use of Approximate Bayesian Computation (ABC) to fit these models without the need to calculate the likelihood, in conjunction with the Deviance Information Criterion (DIC) for model selection. ABC works by simulating artificial data for different parameter values, and comparing the summary statistics of the simulated data to the summary statistics of the observed data. A critical problem is that ABC only works well in lower dimensions, that is, no more than three or four summary statistics should be used. In addition, the choice of the set of statistics is relevant for the accuracy of the parameter estimation. In this presentation, we discuss the process of finding a suitable subset of summary statistics. This work has important applications for the use of ABC in hydrological modelling.