Statistical tools are crucial for a variety of hydrological applications, whether to model processes and enhance understanding and knowledge or to design infrastructure systems. Given the rapid evolution of statistical methods and the need for a solid theoretical foundation for their correct application, a multidisciplinary community STAtistics in HYdrology Working Group (STAHY-WG) aggregated under the International Association of Hydrological Sciences (IAHS) umbrella to contribute to this research field. Now, more than 15 years since its inception, this paper summarizes the main achievements of this productive community collaboration in four (of many) branches of statistical hydrology: extreme value analysis, multivariate analysis, time series analysis, and regionalization. The aim is to provide an overview of recent developments, offer practical suggestions (e.g. software packages), and outline future challenges to support scientists and practitioners in their endeavours within the realm of statistical hydrology studies.@en

What is the “best” model? The answer to this question lies in part in the eyes of the beholder, nevertheless a good model must blend rigorous theory with redeeming qualities such as parsimony and quality of fit. Model selection is used to make inferences, via weighted averaging, from a set of K candidate models, (Formula presented.), and help identify which model is most supported by the observed data, (Formula presented.). Here, we introduce a new and robust estimator of the model evidence, (Formula presented.), which acts as normalizing constant in the denominator of Bayes’ theorem and provides a single quantitative measure of relative support for each hypothesis that integrates model accuracy, uncertainty, and complexity. However, (Formula presented.) is analytically intractable for most practical modeling problems. Our method, coined GAussian Mixture importancE (GAME) sampling, uses bridge sampling of a mixture distribution fitted to samples of the posterior model parameter distribution derived from MCMC simulation. We benchmark the accuracy and reliability of GAME sampling by application to a diverse set of multivariate target distributions (up to 100 dimensions) with known values of (Formula presented.) and to hypothesis testing using numerical modeling of the rainfall-runoff transformation of the Leaf River watershed in Mississippi, USA. These case studies demonstrate that GAME sampling provides robust and unbiased estimates of the evidence at a relatively small computational cost outperforming commonly used estimators. The GAME sampler is implemented in the MATLAB package of DREAM and simplifies considerably scientific inquiry through hypothesis testing and model selection.

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