arXiv subjects

Mark Naylor

Publications and source records attributed to Mark Naylor.

5 recordsLinked to original sources

arXiv2025

Influence of river incision on landslides triggered in Nepal by the Gorkha earthquake: Results from a pixel-based susceptibility model using inlabru

This study presents a comprehensive framework for modelling earthquake-induced landslides (EQILs) through a channel-based analysis of landslide centroid distributions. A key innovation is the incorporation of the normalised channel steepness index ($k_{sn}$) as a physically meaningful and novel covariate, inferring hillslope erosion and fluvial incision processes. Used within spatial point process models, $k_{sn}$ supports the generation of landslide susceptibility maps with quantified uncertainty. To address spatial data misalignment between covariates and landslide observations, we leverage the inlabru framework, which enables coherent integration through mesh-based disaggregation, thereby overcoming challenges associated with spatially misaligned data integration. Our modelling strategy explicitly prioritises prospective transferability to unseen geographical regions, provided that explanatory variable data are available. By modelling both landslide locations and sizes, we find that elevated $k_{sn}$ is strongly associated with increased landslide susceptibility but not with landslide magnitude. The best-fitting Bayesian model, validated through cross-validation, offers a scalable and interpretable solution for predicting earthquake-induced landslides in complex terrain.

stat.AP↗

arXiv2025

Coherent Disaggregation and Uncertainty Quantification for Spatially Misaligned Data

Spatial misalignment arises when datasets are aggregated or collected at different spatial scales, leading to information loss. We develop a Bayesian disaggregation framework that links misaligned data to a continuous-domain model through an iteratively linearised integration scheme implemented with the Integrated Nested Laplace Approximation (INLA). The framework accommodates different ways of handling observations depending on the application, resulting in four variants: (i) \textit{Raster at Full Resolution}, (ii) \textit{Raster Aggregation}, (iii) \textit{Polygon Aggregation} (PolyAgg), and (iv) \textit{Point Values} (PointVal). The first three represent increasing levels of spatial averaging, while the last two address situations with incomplete covariate information. For PolyAgg and PointVal, we reconstruct the covariate field using three strategies -- \textit{Value Plugin}, \textit{Joint Uncertainty}, and \textit{Uncertainty Plugin} -- with the latter two propagating uncertainty. We illustrate the framework with an example motivated by landslide modelling, focusing on methodology rather than interpreting landslide processes. Simulations show that uncertainty-propagating approaches outperform \textit{Value Plugin} method and remain robust under model misspecification. Point-pattern observations and full-resolution covariates are therefore preferable, and when covariate fields are incomplete, uncertainty-aware methods are most reliable. The framework is well suited to landslide susceptibility modelling and other spatial mapping tasks, and integrates seamlessly with INLA-based tools.

stat.ME↗

arXiv2022

Bayesian modelling of the temporal evolution of seismicity using the ETAS.inlabru R-package

The Epidemic Type Aftershock Sequence (ETAS) model is widely used to model seismic sequences and underpins Operational Earthquake Forecasting (OEF). However, it remains challenging to assess the reliability of inverted ETAS parameters for a range of reasons. The most common algorithms just return point estimates with little quantification of uncertainty, and Bayesian Markov Chain Monte Carlo implementations remain slow to run, do not scale well and few have been extended to include spatial structure. Here we present a new approach to ETAS modelling using an alternative Bayesian method, the Integrated Nested Laplace Approximation (INLA). We have implemented this model in a new R-Package called ETAS.inlabru, which builds on the R packages R-INLA and inlabru . Whilst we just present the temporal component here, the model scales to a spatio-temporal model and may include a variety of spatial covariates. Using a series of synthetic case studies, we explore the robustness of our ETAS inversion method. We demonstrate that reliable estimates of the model parameters require that the catalogue data contains periods of relative quiescence as well as triggered sequences. We explore the robustness under stochastic uncertainty in the training data and show that the method is robust to a wide range of starting conditions. We show how the inclusion of historic earthquakes prior to the modelled domain affects the quality of the inversion. Finally, we show that rate dependent incompleteness after large earthquakes has a significant and detrimental effect on the ETAS posteriors. We believe that the speed of the inlabru inversion, which include a rigorous estimation of uncertainty, will enable a deeper exploration of how to use ETAS robustly for seismicity modelling and operational earthquake forecasting.

stat.AP↗

arXiv2022

Approximation of bayesian Hawkes process models with Inlabru

Hawkes process are very popular mathematical tools for modelling phenomena exhibiting a \textit{self-exciting} or \textit{self-correcting} behaviour. Typical examples are earthquakes occurrence, wild-fires, drought, capture-recapture, crime violence, trade exchange, and social network activity. The widespread use of Hawkes process in different fields calls for fast, reproducible, reliable, easy-to-code techniques to implement such models. We offer a technique to perform approximate Bayesian inference of Hawkes process parameters based on the use of the R-package \inlabru. The \inlabru R-package, in turn, relies on the INLA methodology to approximate the posterior of the parameters. Our Hawkes process approximation is based on a decomposition of the log-likelihood in three parts, which are linearly approximated separately. The linear approximation is performed with respect to the mode of the parameters' posterior distribution, which is determined with an iterative gradient-based method. The approximation of the posterior parameters is therefore deterministic, ensuring full reproducibility of the results. The proposed technique only requires the user to provide the functions to calculate the different parts of the decomposed likelihood, which are internally linearly approximated by the R-package \inlabru. We provide a comparison with the \bayesianETAS R-package which is based on an MCMC method. The two techniques provide similar results but our approach requires two to ten times less computational time to converge, depending on the amount of data.

stat.CO↗

arXiv2021

Ranking earthquake forecasts using proper scoring rules: Binary events in a low probability environment

Operational earthquake forecasting for risk management and communication during seismic sequences depends on our ability to select an optimal forecasting model. To do this, we need to compare the performance of competing models with each other in prospective forecasting mode, and to rank their performance using a fair, reproducible and reliable method. The Collaboratory for the Study of Earthquake Predictability (CSEP) conducts such prospective earthquake forecasting experiments around the globe. One metric that has been proposed to rank competing models is the Parimutuel Gambling score, which has the advantage of allowing alarm-based (categorical) forecasts to be compared with probabilistic ones. Here we examine the suitability of this score for ranking competing earthquake forecasts. First, we prove analytically that this score is in general improper, meaning that, on average, it does not prefer the model that generated the data. Even in the special case where it is proper, we show it can still be used in an improper way. Then, we compare its performance with two commonly-used proper scores (the Brier and logarithmic scores), taking into account the uncertainty around the observed average score. We estimate the confidence intervals for the expected score difference which allows us to define if and when a model can be preferred. Our findings suggest the Parimutuel Gambling score should not be used to distinguishing between multiple competing forecasts. They also enable a more rigorous approach to distinguish between the predictive skills of candidate forecasts in addition to their rankings.

stat.AP↗