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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…

Machine Learning · Computer Science 2022-03-31 Mojmír Mutný , Andreas Krause

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to…

Machine Learning · Computer Science 2024-01-29 Yongsheng Mei , Mahdi Imani , Tian Lan

An important task in the statistical analysis of inhomogeneous point processes is to investigate the influence of a set of covariates on the point-generating mechanism. In this article, we consider the nonparametric Bayesian approach to…

Methodology · Statistics 2026-01-19 Patric Dolmeta , Matteo Giordano

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…

Machine Learning · Statistics 2015-06-30 Yves-Laurent Kom Samo , Stephen Roberts

Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM)…

Methodology · Statistics 2019-07-09 Junxian Geng , Wei Shi , Guanyu Hu

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

Computation · Statistics 2018-03-15 Hongqiao Wang , Jinglai Li

The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point patterns. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the…

Computation · Statistics 2017-01-05 Ming Teng , Farouk S. Nathoo , Timothy D. Johnson

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…

Statistics Theory · Mathematics 2020-05-21 Shota Gugushvili , Ester Mariucci , Frank van der Meulen

In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is…

Applications · Statistics 2019-02-19 Ye Liang , Yang Li , Bin Zhang

The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables…

Machine Learning · Statistics 2014-02-20 Thomas A. Lasko

There is a lack of point process models on linear networks. For an arbitrary linear network, we consider new models for a Cox process with an isotropic pair correlation function obtained in various ways by transforming an isotropic Gaussian…

Statistics Theory · Mathematics 2024-01-17 Jesper Møller , Jakob G. Rasmussen

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…

Computation · Statistics 2009-12-25 Ryan Prescott Adams , Iain Murray , David J. C. MacKay

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few…

Machine Learning · Statistics 2018-04-04 S. T. John , James Hensman

Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate.…

Methodology · Statistics 2018-07-03 M. I. Borrajo , W. González-Manteiga , M. D. Martínez-Miranda

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,…

Applications · Statistics 2016-11-29 Shinichiro Shirota , Alan E. Gelfand

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Methodology · Statistics 2022-03-29 Ali Rafei , Michael R. Elliott , Carol A. C. Flannagan

Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…

Computation · Statistics 2015-03-20 S. L. Cotter , G. O. Roberts , A. M. Stuart , D. White

We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…

Statistics Theory · Mathematics 2013-06-14 Mathieu Sart

Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity…

Machine Learning · Statistics 2017-06-27 Seth Flaxman , Yee Whye Teh , Dino Sejdinovic

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…

Statistics Theory · Mathematics 2015-06-08 Shota Gugushvili , Frank van der Meulen , Peter Spreij