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We introduce a novel class of non-stationary covariance functions for random fields on linear networks that allows both the variance and the correlation range of the random field to vary spatially. The proposed covariance functions are…

We present an approach to estimate distance-dependent heterogeneous associations between point-referenced exposures to built environment characteristics and health outcomes. By estimating associations that depend non-linearly on distance…

With advances in sequencing technologies, there are now massive amounts of genomic data from across all life, leading to the possibility that a robust Tree of Life can be constructed. However, "gene tree heterogeneity", which is when…

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…

Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain…

Individuals do not respond uniformly to treatments, events, or interventions. Sociologists routinely partition samples into subgroups to explore how the effects of treatments vary by covariates like race, gender, and socioeconomic status.…

Spatial association and heterogeneity are two critical areas in the research about spatial analysis, geography, statistics and so on. Though large amounts of outstanding methods has been proposed and studied, there are few of them tend to…

We model the spatial dynamics of a forest stand by using a special class of spatio-temporal point processes, the sequential spatial point process, where the spatial dimension is parameterized and the time component is atomic. The sequential…

Rich new marked point process data allow researchers to consider disparate problems such as the factors affecting the location and type of police use of force incidents, and the characteristics that impact the location and size of forest…

This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the…

Nonlinear plant-scale interactions controlling the soil-water balance are generally not valid at larger spatial scales due to spatial heterogeneity in rainfall and vegetation type. The relationships between spatially averaged variables are…

Recently, inhomogeneous generalisations of the Friedmann-Lemaitre-Robertson-Walker cosmological models have gained interest in the astrophysical community and are more often employed to study cosmological phenomena. However, in many papers…

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…

Environmental data may be "large" due to number of records, number of covariates, or both. Random forests has a reputation for good predictive performance when using many covariates with nonlinear relationships, whereas spatial regression,…

In modern spatial statistics, the structure of data that is collected has become more heterogeneous. Depending on the type of spatial data, different modeling strategies for spatial data are used. For example, a kriging approach for…

We aim to link random fields and marked point processes and therefore introduce a new class of stochastic processes which are defined on a random set in R^d. Unlike for random fields, the mark covariance function of a marked random set is…

In neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements…