Exact Bayesian Inference in Spatiotemporal Cox Processes Driven by Multivariate Gaussian Processes

Gonçalves, Flávio B.; Friel, Nial

doi:10.1111/rssb.12237

Cited by 46 publications

(57 citation statements)

References 34 publications

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“…We follow the sampling algorithm in Section 4.2 in Gonçalves and Gamerman (). Unknown quantities to be sampled include

scriptU, K, λ^{*}, z false({scriptS}_{a u g} false), θ

, and we denote them by ψ .…”

Section: Inferencementioning

confidence: 99%

“…Gonçalves and Gamerman () discuss identifiability of λ ∗ . Gibbs sampling for λ ∗ from its full conditional distribution is available when a Gamma prior is assumed, that is,

π false(λ^{*} false) = scriptG false(α, β false)

.…”

Section: Inferencementioning

confidence: 99%

“…The time varying case is easily accommodated through, for example, a time dependent Gamma prior

π false(λ_{t}^{*} false) = scriptG false(α_{t}, β_{t} false)

where

λ_{t}^{*}

varies independently across time. Another extension, which incorporates time dependence among

λ_{t}^{*}

s, introduces Markov structure

λ_{1}^{*} \sim scriptG false(a_{1}, b_{1} false)

λ_{t}^{*} false| K_{1 : t - 1}, λ_{t - 1}^{*} = w^{- 1} λ_{t - 1}^{*} ζ_{t}

and ζ t ∼Beta( wa t ,(1 − w ) a t ), which yields tractable full conditional distributions (Gonçalves and Gamerman, ).…”

Section: Inferencementioning

confidence: 99%

“…Section 2 reviews some Bayesian inference approaches for LGCPs. Section 3 introduces the space‐time exGCP by Gonçalves and Gamerman () and NNGP by Datta et al . ().…”

Section: Introductionmentioning

confidence: 99%

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Scalable inference for space‐time Gaussian Cox processes

Shirota

Banerjee

2019

Journal Time Series Analysis

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The log‐Gaussian Cox process is a flexible and popular stochastic process for modeling point patterns exhibiting spatial and space‐time dependence. Model fitting requires approximation of stochastic integrals which is implemented through discretization over the domain of interest. With fine scale discretization, inference based on Markov chain Monte Carlo is computationally burdensome because of the cost of matrix decompositions and storage, such as the Cholesky, for high dimensional covariance matrices associated with latent Gaussian variables. This article addresses these computational bottlenecks by combining two recent developments: (i) a data augmentation strategy that has been proposed for space‐time Gaussian Cox processes that is based on exact Bayesian inference and does not require fine grid approximations for infinite dimensional integrals, and (ii) a recently developed family of sparsity‐inducing Gaussian processes, called nearest‐neighbor Gaussian processes, to avoid expensive matrix computations. Our inference is delivered within the fully model‐based Bayesian paradigm and does not sacrifice the richness of traditional log‐Gaussian Cox processes. We apply our method to crime event data in San Francisco and investigate the recovery of the intensity surface.

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“…We follow the sampling algorithm in Section 4.2 in Gonçalves and Gamerman (). Unknown quantities to be sampled include

scriptU, K, λ^{*}, z false({scriptS}_{a u g} false), θ

, and we denote them by ψ .…”

Section: Inferencementioning

confidence: 99%

“…Gonçalves and Gamerman () discuss identifiability of λ ∗ . Gibbs sampling for λ ∗ from its full conditional distribution is available when a Gamma prior is assumed, that is,

π false(λ^{*} false) = scriptG false(α, β false)

.…”

Section: Inferencementioning

confidence: 99%

“…The time varying case is easily accommodated through, for example, a time dependent Gamma prior

π false(λ_{t}^{*} false) = scriptG false(α_{t}, β_{t} false)

where

λ_{t}^{*}

varies independently across time. Another extension, which incorporates time dependence among

λ_{t}^{*}

s, introduces Markov structure

λ_{1}^{*} \sim scriptG false(a_{1}, b_{1} false)

λ_{t}^{*} false| K_{1 : t - 1}, λ_{t - 1}^{*} = w^{- 1} λ_{t - 1}^{*} ζ_{t}

and ζ t ∼Beta( wa t ,(1 − w ) a t ), which yields tractable full conditional distributions (Gonçalves and Gamerman, ).…”

Section: Inferencementioning

confidence: 99%

“…Section 2 reviews some Bayesian inference approaches for LGCPs. Section 3 introduces the space‐time exGCP by Gonçalves and Gamerman () and NNGP by Datta et al . ().…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scalable inference for space‐time Gaussian Cox processes

Shirota

Banerjee

2019

Journal Time Series Analysis

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show abstract

“…[8] proposes an exact estimation method to deal with a modification of such a point process which they term the sigmoidal Gaussian Cox process. To avoid discretization of the spatial domain, [9] proposed a Markov chain Monte Carlo algorithm that samples from the joint posterior distribution of the LGCP model. A particular choice of the dominating measure is used to obtain the likelihood function without discretization and this is shown to be crucial to devise a valid MCMC algorithm.…”

Section: Introductionmentioning

confidence: 99%

Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods

Teng

Nathoo²,

Johnson

2017

Journal of Statistical Computation and Simulation

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The Log-Gaussian Cox Process is a commonly used model for the analysis of spatial point pattern data. Fitting this model is difficult because of its doubly-stochastic property, i.e., it is an hierarchical combination of a Poisson process at the first level and a Gaussian Process at the second level. Various methods have been proposed to estimate such a process, including traditional likelihood-based approaches as well as Bayesian methods. We focus here on Bayesian methods and several approaches that have been considered for model fitting within this framework, including Hamiltonian Monte Carlo, the Integrated nested Laplace approximation, and Variational Bayes. We consider these approaches and make comparisons with respect to statistical and computational efficiency. These comparisons are made through several simulation studies as well as through two applications, the first examining ecological data and the second involving neuroimaging data.

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A spatial functional count model for heterogeneity analysis in time

Torres-Signes

Frías

Mateu

et al. 2021

Stoch Environ Res Risk Assess

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A spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in time, and spectral analysis in space. Specifically, model fitting is achieved by minimising the information divergence or relative entropy between the multiscale model underlying the data and the corresponding candidates in the spatial spectral domain. A simulation study is carried out within the family of log-Gaussian Spatial Autoregressive 2 -valued processes (SAR 2 processes) to illustrate the asymptotic properties of the proposed spatial functional estimators. We apply our modelling strategy to spatiotemporal prediction of respiratory disease mortality.

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Exact Bayesian Inference in Spatiotemporal Cox Processes Driven by Multivariate Gaussian Processes

Cited by 46 publications

References 34 publications

Scalable inference for space‐time Gaussian Cox processes

Scalable inference for space‐time Gaussian Cox processes

Bayesian computation for Log-Gaussian Cox processes: a comparative analysis of methods

A spatial functional count model for heterogeneity analysis in time

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