A Comparison of Empirical Bayes and Reference Prior Methods for Spatio-Temporal Data Analysis

AbstractIn Bayesian analysis of spatio-temporal data, the problem of selecting prior distribution for model parameters is of great demand. This paper considers two most popular approaches, empirical Bayes and reference prior, for Bayesian inference. We then use simulation to compare the frequentist properties of these two methods. Since, posterior propriety of the reference prior is only established under separable correlation models, this comparison is concentrated on this case

Importance of Outlier Detection in Spatial Analysis of Wind Erosion

AbstractSpatial outliers in wind erosion are associated with severe weather events so, high rate of erosion or sedimentation in relevance to their spatial vicinity is called outlier. The aim of this paper is to investigate the influence of outliers on variogram model and their parameters in east of Iran. For measuring of soil erosion and sedimentation, some pins were established in nested grids. Decreasing and increasing of pin height, show sedimentation and erosion, respectively. Spatial analysis illustrate that outliers locate in NW-SE direction roughly in the same direction of predominant wind. The maximum amount of outlier is 22cm soil sedimentation

Optimal network design for spatial prediction of soil redistribution (137Cs) based on a minimax approach

Measuring 137Cs is considered an effective method to study soil redistribution rate and hence needs sampling at a number of sites. The spatial configuration of the network of sites to be sampled has a substantial effect on the soil redistribution assessment. Here, motivated by sampling 137Cs, we adopted a model-based approach. For this, we chose the average kriging variance (AKV) as a design criterion. In fact, by minimizing the AKV of soil 137Cs prediction in the paired sub-catchments of Iran's Golestan province, we determined the optimal sampling design in the case that no directly measured prior information of the primary variable of interest (137Cs) is available. However, the AKV depends on some unknown parameters and preliminary estimates of model parameters are not available. To overcome this problem, we apply the minimax approach which minimizes the maximum value of design criterionover the misspecification of parameters. The method is illustrated taking into account the ancillary information (slope%) from representative Sub-catchments (Sample and Testifier, each around 190 ha in size). A simulated annealing algorithm is used to search for an optimal design from among all possible designs. Since, the number of sampling points is often limited by time and budgetary constraints, we use a sequential-based method for selecting the sample size. It is shown that 60 sites are sufficient for the proposed Sample and Testifier sub-catchments

Spatio-temporal modeling and prediction of CO concentrations in Tehran city

One of the most important agents responsible for high pollution in Tehran is carbon monoxide. Prediction of carbon monoxide is of immense help for sustaining the inhabitants’ health level. In this paper, motivated by the statistical analysis of carbon monoxide using the empirical Bayes approach, we deal with the issue of prior specification for the model parameters. In fact, the hyperparameters (the parameters of the prior law) are estimated based on a sampling-based method which depends only on the specification of the marginal spatial and temporal correlation structures. We compare the predictive performance of this approach with the type II maximum likelihood method. Results indicate that the proposed procedure performs better for this data set.