Related papers: Level set Cox processes
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.…
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…
Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin…
The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without…
This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…
This work proposes a scalable probabilistic latent variable model based on Gaussian processes (Lawrence, 2004) in the context of multiple observation spaces. We focus on an application in astrophysics where data sets typically contain both…
Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and…
We study approximations of non-Gaussian stationary processes having long range correlations with microcanonical models. These models are conditioned by the empirical value of an energy vector, evaluated on a single realization. Asymptotic…
In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…
In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…
We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology develops high dimensional data understanding in the point process setting. The method is based on modelling the…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified…
This work introduces a novel approach for generating conditional probabilistic rainfall forecasts with temporal and spatial dependence. A two-step procedure is employed. Firstly, marginal location-specific distributions are jointly…
We study adaptive sensing of Cox point processes, a widely used model from spatial statistics. We introduce three tasks: maximization of captured events, search for the maximum of the intensity function and learning level sets of the…
We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…
We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…
Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…