Related papers: Exact Bayesian Gaussian Cox Processes Using Random…
The log-Gaussian Cox process is a flexible and popular class of point pattern models for capturing spatial and space-time dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented…
Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…
We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…
Prediction of events such as part replacement and failure events plays a critical role in reliability engineering. Event stream data are commonly observed in manufacturing and teleservice systems. Designing predictive models for individual…
We derive the posterior contraction rate for non-parametric Bayesian estimation of the intensity function of a Poisson point process.
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not…
Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
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…
The Power Law Process, also known as Non-Homogeneous Poisson Process, has been used in various aspects, one of which is the software reliability assessment. Specifically, by using its intensity function to compute the rate of change of a…
Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…
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…