Spatiotemporal prediction for log-Gaussian Cox processes

Anders Brix, Peter J. Diggle

Research output: Contribution to journalArticle

Abstract

Space-time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems. We describe a flexible class of space-time point processes. Our models are Cox processes whose stochastic intensity is a space-time Ornstein-Uhlenbeck process. We develop moment-based methods of parameter estimation, show how to predict the underlying intensity by using a Markov chain Monte Carlo approach and illustrate the performance of our methods on a synthetic data set.

Original languageEnglish (US)
Pages (from-to)823-841
Number of pages19
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume63
Issue number4
StatePublished - 2001
Externally publishedYes

Fingerprint

Cox Process
Gaussian Process
Space-time
Prediction
Stochastic Intensity
Ornstein-Uhlenbeck Process
Geographic Information Systems
Point Process
Synthetic Data
Markov Chain Monte Carlo
Parameter Estimation
Moment
Predict
Cox process
Model

Keywords

  • Markov process
  • Metropolis adjusted Langevin algorithm
  • Ornstein-Uhlenbeck process
  • Space-time point process

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Spatiotemporal prediction for log-Gaussian Cox processes. / Brix, Anders; Diggle, Peter J.

In: Journal of the Royal Statistical Society. Series B: Statistical Methodology, Vol. 63, No. 4, 2001, p. 823-841.

Research output: Contribution to journalArticle

@article{47f5a98a9d6041489eae6aa0848c97fc,
title = "Spatiotemporal prediction for log-Gaussian Cox processes",
abstract = "Space-time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems. We describe a flexible class of space-time point processes. Our models are Cox processes whose stochastic intensity is a space-time Ornstein-Uhlenbeck process. We develop moment-based methods of parameter estimation, show how to predict the underlying intensity by using a Markov chain Monte Carlo approach and illustrate the performance of our methods on a synthetic data set.",
keywords = "Markov process, Metropolis adjusted Langevin algorithm, Ornstein-Uhlenbeck process, Space-time point process",
author = "Anders Brix and Diggle, {Peter J.}",
year = "2001",
language = "English (US)",
volume = "63",
pages = "823--841",
journal = "Journal of the Royal Statistical Society. Series B: Statistical Methodology",
issn = "1369-7412",
publisher = "Wiley-Blackwell",
number = "4",

}

TY - JOUR

T1 - Spatiotemporal prediction for log-Gaussian Cox processes

AU - Brix, Anders

AU - Diggle, Peter J.

PY - 2001

Y1 - 2001

N2 - Space-time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems. We describe a flexible class of space-time point processes. Our models are Cox processes whose stochastic intensity is a space-time Ornstein-Uhlenbeck process. We develop moment-based methods of parameter estimation, show how to predict the underlying intensity by using a Markov chain Monte Carlo approach and illustrate the performance of our methods on a synthetic data set.

AB - Space-time point pattern data have become more widely available as a result of technological developments in areas such as geographic information systems. We describe a flexible class of space-time point processes. Our models are Cox processes whose stochastic intensity is a space-time Ornstein-Uhlenbeck process. We develop moment-based methods of parameter estimation, show how to predict the underlying intensity by using a Markov chain Monte Carlo approach and illustrate the performance of our methods on a synthetic data set.

KW - Markov process

KW - Metropolis adjusted Langevin algorithm

KW - Ornstein-Uhlenbeck process

KW - Space-time point process

UR - http://www.scopus.com/inward/record.url?scp=0035649290&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035649290&partnerID=8YFLogxK

M3 - Article

VL - 63

SP - 823

EP - 841

JO - Journal of the Royal Statistical Society. Series B: Statistical Methodology

JF - Journal of the Royal Statistical Society. Series B: Statistical Methodology

SN - 1369-7412

IS - 4

ER -