Predictive Inference for Spatio-temporal Precipitation Data and Its Extremes

Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and subject to substaintial skewness which often arise in measurements of many environmental processes, and we apply the method to precipitation data in south-west Western Australia. A generalised hyperbolic Bayesian hierarchical model is constructed for the intensity, frequency and duration of daily precipitation, including the extremes. Unlike models based on extreme value theory, which only model maxima of finite-sized blocks or exceedances above a large threshold, the proposed model uses all the data available efficiently, and hence not only fits the extremes but also models the entire rainfall distribution. It captures spatial and temporal clustering, as well as spatially and temporally varying volatility and skewness. The model assumes that the regional precipitation is driven by a latent process characterised by geographical and climatological covariates. Effects not fully described by the covariates are captured by spatial and temporal structure in the hierarchies. Inference is provided by MCMC using a Metropolis-Hastings algorithm and spatial interpolation method, which provide a natural approach for estimating uncertainty. Similarly both spatial and temporal predictions with uncertainty can be produced with the model.Comment: Under review at Journal of the American Statistical Association. 27 pages, 10 figure

A disposition of interpolation techniques

A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated values, 3) incorporation of ancillary information, and 4) incorporation of process knowledge. The described methods include inverse distance weighting, nearest neighbour methods, geostatistical interpolation methods, Kalman filter methods, Bayesian Maximum Entropy methods, etc. The applicability of methods in aggregation (upscaling) and disaggregation (downscaling) is discussed. Software for interpolation is described. The application of interpolation techniques is illustrated in two case studies: temporal interpolation of indicators for ecological water quality, and spatio-temporal interpolation and aggregation of pesticide concentrations in Dutch surface waters. A valuable next step will be to construct a decision tree or decision support system, that guides the environmental scientist to easy-to-use software implementations that are appropriate to solve their interpolation problem. Validation studies are needed to assess the quality of interpolated values, and the quality of information on uncertainty provided by the interpolation method

A Scalable MCEM Estimator for Spatio-Temporal Autoregressive Models

Very large spatio-temporal lattice data are becoming increasingly common across a variety of disciplines. However, estimating interdependence across space and time in large areal datasets remains challenging, as existing approaches are often (i) not scalable, (ii) designed for conditionally Gaussian outcome data, or (iii) are limited to cross-sectional and univariate outcomes. This paper proposes an MCEM estimation strategy for a family of latent-Gaussian multivariate spatio-temporal models that addresses these issues. The proposed estimator is applicable to a wide range of non-Gaussian outcomes, and implementations for binary and count outcomes are discussed explicitly. The methodology is illustrated on simulated data, as well as on weekly data of IS-related events in Syrian districts.Comment: 29 pages, 8 figure