Generalised additive point process models for natural hazard occurrence

Abstract

Point processes are a natural class of models for representing occurrences of various types of natural hazard event. Flexibly implementing such models is often hindered by intractable likelihood forms. Consequently, the rates of point processes tend to be reduced to parametric forms, or the processes are discretised to give data of readily modelled “count‐per‐unit” type. This work proposes generalised additive model forms for point process rates. The resulting low‐rank spatiotemporal representations of rates, coupled with the Laplace approximation, makes the restricted likelihood relatively tractable and hence inference for such models possible. The models can also be interpreted from a regression perspective. The proposed models are used to estimate different types of Cox process and then spatiotemporal variation in European windstorms. Through a combination of thin‐plate and cubic regression splines and their tensor product, established relationships between where windstorms occur and the state of the North Atlantic Oscillation are confirmed and then expanded to bring detailed understanding of within‐year variation, which has otherwise not been possible with count‐based models.

Quantifying effect of geological factor on distribution of earthquake occurrences by inhomogeneous Cox processes

“…To involve geological factors in the analysis from different perspectives, one could consider for future research the non parametric estimation (e.g. Baddeley et al, 2012) or semi parametric modeling such as generalized additive models (Youngman and Economou, 2017). Finally, we perform backward elimination to select the important geological variables.…”

Spatial co‐localisation of extreme weather events: a clear and present danger

“…Generalised Additive Models or GAMs (Wood, 2017) were adopted as the modelling framework to characterise the trends in extreme event frequency. This well‐established class of models allows for flexible characterisation of the spatio‐temporal variability of a modelled environmental variable and has been used extensively to characterise natural hazards (Youngman and Economou, 2017) and in modelling environmental variables more generally (Wood, 2017). The data extracted relates to counts of events in grid cell and year.…”

Improving our understanding of wind extremes from Bangladesh tropical cyclones: insights from a high-resolution convection-permitting numerical model

“…To condense information from all 9 regional model ensemble member footprints into a coherent spatial summary of the tropical cyclone hazard, we use a generalised additive model (GAM), after Hastie & Tibshirani (1986), based on the R package mgcv of Wood (2017), as a flexible spatial regression framework. GAMs are an extension of generalised linear modelling that use smooth functions of covariates to build a linear predictor and have previously been applied in similar geospatial natural hazard assessments, such as storm count data over Europe (Youngman and Economou, 2017), spatial prediction of maximum wind speed over Switzerland (Etienne et al, 2010) and return level estimation for U.S. wind gusts (Youngman, 2019). In each case, these studies incorporate spatial information into the GAMs formation, thereby implicitly respecting the spatial interaction present in the source data, and use the spatial dependence as a source of information.…”