  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.
