Joint modeling of landslide counts and sizes using spatial marked point processes with sub-asymptotic mark distributions

TL;DR

This paper introduces a Bayesian hierarchical model that jointly predicts landslide counts and sizes using spatial marked point processes with sub-asymptotic distributions, improving large landslide size predictions for hazard mapping.

Contribution

It develops a novel joint modeling framework combining extreme-value theory with spatial marked point processes, enhancing landslide hazard assessment accuracy.

Findings

Sub-asymptotic distributions improve large landslide size predictions.

Joint models capture cross-correlation between landslide counts and sizes.

Spatial dependence is effectively modeled using intrinsic CAR priors.

Abstract

To accurately quantify landslide hazard in a region of Turkey, we develop new marked point process models within a Bayesian hierarchical framework for the joint prediction of landslide counts and sizes. To accommodate for the dominant role of the few largest landslides in aggregated sizes, we leverage mark distributions with strong justification from extreme-value theory, thus bridging the two broad areas of statistics of extremes and marked point patterns. At the data level, we assume a Poisson distribution for landslide counts, while we compare different "sub-asymptotic" distributions for landslide sizes to flexibly model their upper and lower tails. At the latent level, Poisson intensities and the median of the size distribution vary spatially in terms of fixed and random effects, with shared spatial components capturing cross-correlation between landslide counts and sizes. We robustly model spatial dependence using intrinsic conditional autoregressive priors. Our novel models are fitted efficiently using a customized adaptive Markov chain Monte Carlo algorithm. We show that, for our dataset, sub-asymptotic mark distributions provide improved predictions of large landslide sizes compared to more traditional choices. To showcase the benefits of joint occurrence-size models and illustrate their usefulness for risk assessment, we map landslide hazard along major roads.