AG Analysis & Stochastik
Prof. Dr. Anita Behme, Prof. Dr. Martin Keller-Ressel, Prof. Dr. Zoltán Sasvári,
Prof. Dr. René Schilling, Prof. Dr. Friedemann Schuricht, Prof. Dr. Ostap Okhrin
Sommer 2024 - Summer term 2024
04.04.2024 |
Dr. Reetam Majumder (Imperial College London) "Modeling Extremal Streamflow using Deep Learning Approximations and a Flexible Spatial Process" Quantifying changes in the probability and magnitude of extreme flooding events is key to mitigating their impacts. While hydrodynamic data are inherently spatially dependent, traditional spatial models such as Gaussian processes are poorly suited for modeling extreme events. Spatial extreme value models with more realistic tail dependence characteristics are under active development. They are theoretically justified, but give intractable likelihoods, making computation challenging for small datasets and prohibitive for continental-scale studies. We propose a process mixture model (PMM) for spatial extremes as a linear interpolation of a Gaussian process and a max-stable process, yielding desirable tail dependence properties but intractable likelihoods. A unique computational strategy to approximate the intractable likelihood is employed, whereby a neural network is embedded in a semi-parametric quantile regression framework. The neural network is trained on synthetic data generated from a dense surface of parameter values, and the surrogate likelihood obtained in this manner is cheap to evaluate afterwards and can be incorporated into a Bayesian hierarchical model. Parameter estimation is carried out using Markov Chain Monte Carlo methods. The PMM is used to analyze changes in annual maximum streamflow within the US over the last 50 years, and is able to detect areas which show increases in extreme streamflow over time. |
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13.03.2024 |
Dr. Jordan Richards (University of Edinburgh) "Neural Bayes estimators for likelihood-free and amortised inference for spatial extremes" Likelihood-based inference with spatial extremal dependence models is often infeasible in moderate or high dimensions due to an intractable likelihood function and/or the need for computationally expensive censoring to reduce estimation bias. Neural Bayes estimators are a promising recent approach to inference that uses neural networks to transform data into parameter estimates. They are likelihood-free, inherit the optimality properties of Bayes estimators, and are substantially faster than classical methods. Neural Bayes estimators are adapted for peaks-over-threshold dependence models; in particular, a methodology is developed for coping with the computational challenges often encountered when modelling spatial extremes (e.g., censoring). Substantial improvements are demonstrated in computational and statistical efficiency relative to conventional likelihood-based approaches using popular extremal dependence models, including max-stable and r-Pareto processes and random scale mixtures. The application to Arabian PM2.5 concentrations illustrates the significant computational advantages of using the estimator over traditional likelihood-based techniques, as it requires fitting over 100 million spatial extremal dependence models. |
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