Related papers: Nonparametric inference for nonstationary spatial …
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…
The log-Gaussian Cox process (LGCP) is a popular point process for modeling non-interacting spatial point patterns. This paper extends the LGCP model to handle data exhibiting fundamentally different behaviors in different subregions of the…
Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates.…
We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…
We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
We view the locations and times of a collection of crime events as a space-time point pattern. So, with either a nonhomogeneous Poisson process or with a more general Cox process, we need to specify a space-time intensity. For the latter,…
This paper introduces a new modelling framework for multivariate anisotropic Cox processes. Building on recent innovations in multivariate spatial statistics, we propose a new family of multivariate anisotropic random fields and construct a…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the…
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…
We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the…
In spite of the diverse literature on nonstationary spatial modeling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets…
The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…
In spatio-temporal analysis, we often record data at specific time intervals but with varying spatial locations between these timepoints. We propose a conditional model to analyze such spatio-temporal data that accommodates the dependencies…
This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise…