Modeling mountain accidents and assessing risk through spatio-temporal point processes

Abstract

Historically, mountain activities have been associated to accidents, injuries and fatalities. The spatial and temporal context, however, has been largely neglected, with most studies focusing on proximal causes of accidents. The objective of the present study is to analyse the effects of spatial and temporal covariables on the distribution of mountain accidents in a specific area over a span of 11 years. The current dataset includes 572 rescues on Montserrat Natural Protected Area between 2011 and 2021 and comprises 249 climbing rescues and 310 hiking rescues. We assume that mountain accidents follow a Log-Gaussian Cox Process (LGCP) and we consider an empirical analysis of the first-order characteristics. Then we propose a model in which the conditional intensity of the point process depends on some specific spatial and temporal covariables affecting the distribution of this space-time point pattern. We use the inhomogeneous spatio-temporal K-function to estimate second-order properties. Finally, we model the residual spatio-temporal variation as a stochastic process using a space-time covariance function under a separable space-time structure, and we conduct a risk analysis based on the resulting full LGCP through the Value-at-Risk. The results indicate that rescues are clustered over short distances, typically below 100–300 m. Spatial and temporal predictors differ across activities, while risk remains consistently concentrated in specific areas throughout the study period. Overall, the full LGCP model shows a good fit and is able to generate simulations consistent with the observed data.