|via A. M. Ampère 56 - 20131 Milano (Italy)|
in seismic hazard assessment
(i) Basic features of the earthquake process. Catalogue data. The role of stochastic models. Point process models. The philosophy behind the Statistical Software Library (SSLib).
(ii) Revision of basic features of point processes: fidi distributions, moment densities and measures, counting and interval properties, conditional intensities and likelihoods; space, space-time, and marked point processes.
(iii) The Poisson process: properties and characterisations; non-stationary and spatial versions; simulation, estimation, and testing; uses and implications for earthquake engineering and insurance.
(i) Applications: estimation of seismicity; cluster models; correlation structure.
(ii) Estimation of meant rate (seismicity) for non-homogeneous processes. Smoothing methods. Non-parametric and Bayesian methods.
(iii) Estimation of second order properties. The effects of stationarity and isotropy. Time and space correlation functions.
(i) Applications: estimation, simulation and prediction of point processes; probabilistic earthquake forecasts.
(ii) Background theory: from dependence to independence; conditional expectations and probabilities; point process likelihoods; space, space-time and marked point processes.
(iii) Theoretical background: predictable processes; point process martingales and compensators; formal definitions of likelihoods and conditional intensities.
(iv) Applications to special models: self-exciting and ETAS models; simple and linked stress release models; a point-process setting for the M8 algorithm.
(i) Display and evaluation of probabilistic earthquake forecasts: the importance of geographical display methods; scoring probability forecasts; some theoretical aspects of information gain.
(ii) Self-similarity and fractal dimension. Estimation and interpretation of fractal dimensions from point process data.
(iii) Networks of faults and stochastic network theory. Modelling fault networks for simulation purposes. What are the links with communications networks?
(iv) Spectral methods. The point process spectrum, its properties and estimation. P.p.d. measures.