Fixed Rank Filtering for Spatio-Temporal Data

Cressie, Noel; Shi, Tao; Kang, Emily L.

doi:10.1198/jcgs.2010.09051

Cited by 158 publications

(127 citation statements)

References 30 publications

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“…First, we consider MSPE. Because of the skewness and mean-variance dependence in {M SP E X (T * , l)}, we use a fourth-root transformation to transform the response (Cressie et al, 2010). The boxplots in Figures 10 and 11 show that the distributions of the differences between the fourth-root transformations (superscripts "C" and "H" denote, respectively, analysis under the CSIRS model and under the approximate HSIRS model):…”

Section: Results Of the Simulation Experimentsmentioning

confidence: 99%

Bayesian hierarchical statistical SIRS models

Zhuang

Cressie

2014

Stat Methods Appl

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The classic SIR (susceptible-infectious-recovered) model, has been used extensively to study the dynamical evolution of an infectious disease in a large population. The SIR-susceptible (SIRS) model is an extension of the SIR model to allow modeling imperfect immunity (those who have recovered might become susceptible again). SIR(S) models assume observed counts are "mass balanced. " Here, mass balance means that total count equals the sum of counts of the individual components of the model. However, since the observed counts have errors, we propose a model that assigns the mass balance to the hidden process of a (Bayesian) hierarchical SIRS (HSIRS) model. Another challenge is to capture the stochastic or random nature of an epidemic process in a SIRS. The HSIRS model accomplishes this through modeling the dynam-ical evolution on a transformed scale. Through simulation, we compare the HSIRS model to the classic SIRS (CSIRS) model, a model where it is assumed that the observed counts are mass balanced and the dynamical evolution is deterministic. AbstractThe classic SIR (susceptible-infectious-recovered) model, has been used extensively to study the dynamical evolution of an infectious disease in a large population. The SIR-susceptible (SIRS) model is an extension of the SIR model to allow modeling imperfect immunity (those who have recovered might become susceptible again). SIR(S) models assume observed counts are "mass balanced." Here, mass balance means that total count equals the sum of counts of the individual components of the model. However, since the observed counts have errors, we propose a model that assigns the mass balance to the hidden process of a (Bayesian) hierarchical SIRS (HSIRS) model. Another challenge is to capture the stochastic or random nature of an epidemic process in a SIRS. The HSIRS model accomplishes this through modeling the dynamical evolution on a transformed scale. Through simulation, we compare the HSIRS model to the classic SIRS (CSIRS) model, a model where it is assumed that the observed counts are mass balanced and the dynamical evolution is deterministic.

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Section: Results Of the Simulation Experimentsmentioning

confidence: 99%

Bayesian hierarchical statistical SIRS models

Zhuang

Cressie

2014

Stat Methods Appl

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“…However, it could be extended to a hierarchical spatio-temporal model in an obvious way. We could use the same data model and a process model where the reduced-dimensional basis function coefficients evolve over time (e.g., Wikle et al, 2001;Cressie et al, 2010). There remain the problems of estimation of spatio-temporalmodel parameters and optimal filtering, smoothing, and forecasting from the empirical predictive distribution.…”

Section: Discussionmentioning

confidence: 99%

Hierarchical statistical modeling of big spatial datasets using the exponential family of distributions

Sengupta

Cressie

2013

Spatial Statistics

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Big spatial datasets are very common in scientific problems, such as those involving remote sensing of the earth by satellites, climate-model output, small-area samples from national surveys, and so forth. In this article, our interest lies primarily in very large, non-Gaussian datasets. We consider a hierarchical statistical model consisting of a conditional exponentialfamily model for the data and an underlying (hidden) geostatistical process for some transformation of the (conditional) mean of the data model. Within this hierarchical model, dimension reduction is achieved by modeling the geostatistical process as a linear combination of a fixed number of spatial basis functions, which results in substantial computational speedups. These models do not rely on specifying a spatial-weights matrix, and no assumptions of homogeneity, stationarity, or isotropy are made. Our approach to inference using these models is empirical-Bayesian in nature. We develop maximum likelihood (ML) estimates of the unknown parameters using Laplace approximations in an expectation-maximization (EM) algorithm. We illustrate the performance of the resulting empirical hierarchical model using a simulation study. We also apply our methodology to analyze a remote sensing dataset of aerosol optical depth.

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“…Spatio-temporal processes can now be predicted at large regional and global scales [26,27,28] . Hierarchical statistical modelling relies on the model specifications being appropriate at each level of the hierarchy.…”

Section: From Information To Knowledgementioning

confidence: 99%

Buried treasures

2014

Past, Present, and Future of Statistical Science

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Environmental Informatics uses a panoply of tools from the Statistics, Mathematics, Computing, and Visualisation disciplines. It uses these tools to reveal, quantify, and validate scientific hypotheses in the environmental sciences, with the quantification of uncertainty central to its approach. There is now a strong recognition that scientific models need to incorporate stochastic components throughout: While it has always been recognised that data have a component of measurement error, attention is now being given to the quantification of model error, and it is becoming accepted by environmental scientists that probability models for the latter allows for a coherent way to make scientific inference. In Environmental Informatics, uncertainty may be assigned not only to datasets of measurements, but also to computer-generated climate-model output. Methodological advances, in the form of hierarchical statistical models and the accompanying computational developments, have expanded the scope of statistical analyses into very large spatial domains. This has led to studies of the dynamical evolution of entire spatial fields of geophysical variables, where results are given in terms of predictive distributions. Environmental Informatics is not only involved in characterising the environment, it can also be used to make decisions about mitigation and adaptation strategies. The steps taken by environmental scientists, from data to information, from information to knowledge, and from knowledge to decisions, are all taken in the presence of uncertainty. Environmental Informatics encompasses all these aspects. Abstract Environmental Informatics uses a panoply of tools from the Statistics, Mathematics, Computing, and Visualisation disciplines. It uses these tools to reveal, quantify, and validate scientific hypotheses in the environmental sciences, with the quantification of uncertainty central to its approach. There is now a strong recognition that scientific models need to incorporate stochastic components throughout: While it has always been recognised that data have a component of measurement error, attention is now being given to the quantification of model error, and it is becoming accepted by environmental scientists that probability models for the latter allows for a coherent way to make scientific inference. In Environmental Informatics, uncertainty may be assigned not only to datasets of measurements, but also to computer-generated climate-model output. Methodological advances, in the form of hierarchical statistical models and the accompanying computational developments, have expanded the scope of statistical analyses into very large spatial domains. This has led to studies of the dynamical evolution of entire spatial fields of geophysical variables, where results are given in terms of predictive distributions. Environmental Informatics is not only involved in characterising the environment, it can also be used to make decisions about mitigation and adaptation strategies. The steps taken by environmental...

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Fixed Rank Filtering for Spatio-Temporal Data

Cited by 158 publications

References 30 publications

Bayesian hierarchical statistical SIRS models

Bayesian hierarchical statistical SIRS models

Hierarchical statistical modeling of big spatial datasets using the exponential family of distributions

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