Spatial process modelling for univariate and multivariate dynamic spatial data (original) (raw)

Hierarchical Bayesian Modeling For Spatial Time Series: An Alternative Approach To Spatial Sur

2006

Despite the fact that the amount of datasets containing long economic time series with a spatial reference has significantly increased during the years, the presence of integrated techniques that aim to describe the temporal evolution of the series while accounting for the location of the measurements and their neighboring relations is very sparse in the econometric literature. This paper shows how the Hierarchical Bayesian Space Time model presented by Wikle, Berliner and Cressie (Environmental and Ecological Statistics, l998) for temperature modeling, can be tailored to model relationships between variables that have both a spatial and a temporal reference. The first stage of the hierarchical model includes a set of regression equations (each one corresponding to a different location) coupled with a dynamic space-time process that accounts for the unexplained variation. At the second stage, the regression parameters are endowed with priors that reflect the neighboring relations of the locations under study; moreover, the spatio-temporal dependencies in the dynamic process for the unexplained variation are being established. Putting hyperpriors on previous stages' parameters completes the Bayesian formulation, which can be implemented in a Markov Chain Monte Carlo framework. The proposed modeling strategy is useful in quantifying the temporal evolution in relations between economic variables and this quantification may serve for excess forecasting accuracy.

A HIERARCHICAL BAYESIAN APPROACH FOR SPATIAL TIME SERIES MODELING

real.illinois.edu, 2009

Spatial Time-Series Modeling: A review of the proposed methodologies

The Regional Economics Applications …, 2003

This paper discusses three modeling techniques, which apply to multiple time series data that correspond to different spatial locations (spatial time series). The first two methods, namely the Space-Time ARIMA (STARIMA) and the Bayesian Vector Autoregressive (BVAR) model with spatial priors apply when interest lies on the spatiotemporal evolution of a single variable. The former is better suited for applications of large spatial and temporal dimension whereas the latter can be realistically performed when the number of locations of the study is rather small. Next, we consider models that aim to describe relationships between variables with a spatio-temporal reference and discuss the general class of dynamic space-time models in the framework presented by . Each model class is introduced through a motivating application.

A Generalized Convolution Model for Multivariate Nonstationary Spatial Processes

Statistica Sinica

We propose a flexible class of nonstationary stochastic models for mul-tivariate spatial data. The method is based on convolutions of spatially varying covariance kernels and produces mathematically valid covariance structures. This method generalizes the convolution approach suggested by Majumdar and Gelfand (2007) to extend multivariate spatial covariance functions to the nonstationary case. A Bayesian method for estimation of the parameters in the covariance model based on a Gibbs sampler is proposed, then applied to simulated data. Model comparison is performed with the coregionalization model of Wackernagel (2003) that uses a stationary bivariate model. Based on posterior prediction results, the performance of our model appears to be considerably better.

Nonstationary multivariate process modeling through spatially varying coregionalization

Test, 2004

Models for the analysis of multivariate spatial data are receiving increased attention these days. In many applications it will be preferable to work with multivariate spatial processes to provide such models. A critical specification in developing these models is the cross covariance function. An attractive, constructive approach for creating rich computationally manageable classes of such functions is the linear model of coregionalization (LMC). We begin with a fully Bayesian development of the LMC including the posterior distribution of the component ranges. We offer clarification of the connection between joint and conditional approaches to fitting such models including prior specifications. However, to substantially enhance the usefulness of such modeling we propose the notion of a spatially varying LMC (SVLMC) providing a rich class of multivariate nonstationary processes with simple interpretation. We illustrate the use of our proposed SVLMC with application to more than 600 commercial property transactions in three quite different real estate markets, Chicago, Dallas and San Diego. Bivariate nonstationary process models are developed for income from and selling price of the property.

A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets

STATISTICA SINICA, 2014

When spatio-temporal datasets are large, the computational burden can lead to failures in the implementation of traditional geostatistical tools. In this paper, we propose a computationally efficient Bayesian hierarchical spatio-temporal model in which the spatial dependence is approximated by a Gaussian Markov random field (GMRF) while the temporal correlation is described using a vector autoregressive model. By introducing an auxiliary lattice on the spatial region of interest, the proposed method is not only able to handle irregularly spaced observations in the spatial domain, but it is also able to bypass the missing data problem in a spatio-temporal process. Because the computational complexity of the proposed Markov chain Monte Carlo algorithm is of the order O(n) with n the total number of observations in space and time, our method can be used to handle very large spatio-temporal datasets with reasonable CPU times. The performance of the proposed model is illustrated using simulation studies and a dataset of precipitation data from the coterminous United States.

Modern perspectives on statistics for spatio-temporal data

Wiley Interdisciplinary Reviews: Computational Statistics, 2014

Spatio-temporal statistical models are increasingly being used across a wide variety of scientific disciplines to describe and predict spatially explicit processes that evolve over time. Although descriptive models that approach this problem from the second-order (covariance) perspective are important, many real-world processes are dynamic, and it can be more efficient in such cases to characterize the associated spatio-temporal dependence by the use of dynamical models. The challenge with the specification of such dynamical models has been related to the curse of dimensionality and the specification of realistic dependence structures. Even in fairly simple linear/Gaussian settings, spatio-temporal statistical models are often over parameterized. This problem is compounded when the spatio-temporal dynamical processes are nonlinear or multivariate. Hierarchical models have proven invaluable in their ability to deal to some extent with this issue by allowing dependency among groups of parameters and science-based parameterizations. Such models are best considered from a Bayesian perspective, with associated computational challenges. Spatio-temporal statistics remains an active and vibrant area of research.

Bayesian Spatio-Temporal Modeling for Forecasting, Trend Assessment and Spatial Trend Filtering

2019

This work develops Bayesian spatio-temporal modeling techniques specifically aimed at studying several aspects of our motivating applications; to include vector-borne disease incidence and air pollution levels. A key attribute of the proposed techniques are that they are scalable to extremely large data sets which consist of spatio-temporally oriented observations. Largely, the scalability of our modeling strategies is accomplished in two primary ways. First, through the introduction of carefully constructed latent random variables we are able to develop Markov chain Monte Carlo (MCMC) sampling algorithms that consist primarily of Gibbs steps. This leads to the fast and easy updating of the model parameters from common distributions. Second, for the spatio-temporal aspects of the models, a novel sampling strategy for Gaussian Markov random fields (GRMFs) that can be easily implemented (in parallel) within MCMC sampling algorithms is used. The performance of the proposed modeling str...

Generalized spatial Dirichlet process models

2005

Many models for the study of point-referenced data explicitly introduce spatial random effects to capture residual spatial association. These spatial effects are customarily modelled as a zeromean stationary Gaussian process. The spatial Dirichlet process introduced by Gelfand et al. (2005) produces a random spatial process which is neither Gaussian nor stationary. Rather, it varies about a process that is assumed to be stationary and Gaussian. The spatial Dirichlet process arises as a probability-weighted collection of random surfaces. This can be limiting for modelling and inferential purposes since it insists that a process realization must be one of these surfaces. We introduce a random distribution for the spatial effects that allows different surface selection at different sites. Moreover, we can specify the model so that the marginal distribution of the effect at each site still comes from a Dirichlet process. The development is offered constructively, providing a multivariate extension of the stick-breaking representation of the weights. We then introduce mixing using this generalized spatial Dirichlet process. We illustrate with a simulated dataset of independent replications and note that we can embed the generalized process within a dynamic model specification to eliminate the independence assumption.

Spatial process modelling for univariate and multivariate dynamic spatial data (original) (raw)

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