Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes in<i>R</i>

Taylor, Benjamin M.; Davies, Tilman M.; Rowlingson, Barry; Diggle, Peter J.

doi:10.18637/jss.v063.i07

Cited by 40 publications

(66 citation statements)

References 43 publications

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“…These are relatively diffuse priors, with the exception of the prior for ϕ , which a priori sets the range of spatial dependence to be up to around a fifth of the width of the observation window: this is required to avoid numerical singularities in matrix computations; see Taylor et al . (). Note that the units of ϕ are in latitude and longitude in this example.…”

Section: Application: Analysis Of Health Facility Data In Namibia Witmentioning

confidence: 97%

“…If sampling effort is constant across space, then

W_{ijk} = W_{ij} = \frac{e_{i}}{\sum_{l : A_{i} \cap Ω_{l}^{false(j false)} \neq normal∅} e_{l}},

and we can estimate q ij by drawing independent and identically distributed u 1 ,…, u M ∼Unif( C j ) and using

{\overset{q}{true}}_{ij} = \frac{1}{M} \sum_{l = 1}^{M} \{\frac{e_{i}}{\underset{v : A_{i} \cap {normalΩ}_{v}^{(j)} \neq \emptyset}{false\sum} e_{v}} double-struckI (u_{l} \in {normalΩ}_{k}^{(j)})\} .

This method is implemented as an extension to the R package lgcp (Taylor et al ., ): the main assumption is that the W ijk are known; if this is not so, a pragmatic (but informative) assumption might be W i , j , k = c whence events are allocated at random, i.e. without preference for a particular A i .…”

Section: Aggregated Spatial Models With Non‐trivial Intersection Of Rmentioning

confidence: 99%

“…() and Taylor et al . () to include the case of spatiotemporal‐aggregated data where regional boundaries change over time and may be uncertain. We show how this can be achieved with a simple modification of the multinomial sampling step.…”

Section: Introductionmentioning

confidence: 99%

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Continuous Inference for Aggregated Point Process Data

Taylor

Andrade-Pacheco

Sturrock

2018

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary The paper introduces new methods for inference with count data registered on a set of aggregation units. Such data are omnipresent in epidemiology because of confidentiality issues: it is much more common to know the county in which an individual resides, say, than to know their exact location in space. Inference for aggregated data has traditionally made use of models for discrete spatial variation, e.g. conditional auto‐regressive models. We argue that such discrete models can be improved from both a scientific and an inferential perspective by using spatiotemporally continuous models to model the aggregated counts directly. We introduce methods for delivering (limiting) continuous inference with spatiotemporal aggregated count data in which the aggregation units might change over time and are subject to uncertainty. We illustrate our methods by using two examples: from epidemiology, spatial prediction of malaria incidence in Namibia, and, from politics, forecasting voting under the proposed changes to parliamentary boundaries in the UK.

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Section: Application: Analysis Of Health Facility Data In Namibia Witmentioning

confidence: 97%

“…If sampling effort is constant across space, then

W_{ijk} = W_{ij} = \frac{e_{i}}{\sum_{l : A_{i} \cap Ω_{l}^{false(j false)} \neq normal∅} e_{l}},

and we can estimate q ij by drawing independent and identically distributed u 1 ,…, u M ∼Unif( C j ) and using

{\overset{q}{true}}_{ij} = \frac{1}{M} \sum_{l = 1}^{M} \{\frac{e_{i}}{\underset{v : A_{i} \cap {normalΩ}_{v}^{(j)} \neq \emptyset}{false\sum} e_{v}} double-struckI (u_{l} \in {normalΩ}_{k}^{(j)})\} .

Section: Aggregated Spatial Models With Non‐trivial Intersection Of Rmentioning

confidence: 99%

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Continuous Inference for Aggregated Point Process Data

Taylor

Andrade-Pacheco

Sturrock

2018

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…Taylor et al . () provide a software package for Bayesian inference (MALA and INLA) of spatiotemporal and multivariate LGCP.…”

Section: Cox Processes Driven By Gp: a Brief Reviewmentioning

confidence: 99%

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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“…The corresponding Cox process is known as the LGCP, and it was defined independently by Coles & Jones (), Rathbun () and Møller et al (). More details can be found in Brix & Diggle (), Lawson & Denison (), Møller (), Møller & Waagepetersen, (), Rue et al () and Taylor et al (), including sampling algorithms, estimation procedures and examples, using both the classical and Bayesian approaches.…”

Section: Poisson and Cox Point Process Modelsmentioning

confidence: 99%

Cox Point Processes: Why One Realisation Is Not Enough

Micheas

2018

Int Statistical Rev

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Summary We review a rich class of point process models, Cox point processes, and illustrate the necessity of more than one observation (point patterns) in performing parameter estimation. Furthermore, we introduce a new Cox point process model by treating the intensity function of the underlying Poisson point process as a random mixture of normal components. The behaviour and performance of the new model are compared with those of popular Cox point process models. The new model is exemplified with an application that involves a single point pattern corresponding to earthquake events in California, USA.

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Bayesian Inference and Data Augmentation Schemes for Spatial, Spatiotemporal and Multivariate Log-Gaussian Cox Processes inR

Cited by 40 publications

References 43 publications

Continuous Inference for Aggregated Point Process Data

Continuous Inference for Aggregated Point Process Data

Scalable inference for space‐time Gaussian Cox processes

Cox Point Processes: Why One Realisation Is Not Enough

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