Spatial Design for Knot Selection in Knot-Based Low-Rank Models
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Abstract: (4713 Views) |
Analysis of large geostatistical data sets, usually, entail the expensive matrix computations. This problem creates challenges in implementing statistical inferences of traditional Bayesian models. In addition,researchers often face with multiple spatial data sets with complex spatial dependence structures that their analysis is difficult. This is a problem for MCMC sampling algorithms that are commonly used in Bayesian analysis of spatial models, causing serious problems such as slowing down and chain integration. To escape from such computational problems, we use low-rank models, to analyze Gaussian geostatistical data. This models improve MCMC sampler convergence rate and decrease sampler run-time by reducing parameter space. The idea here is to assume, quite reasonably, that the spatial information available from the entire set of observed locations can be summarized in terms of a smaller, but representative, sets of locations, or ‘knots’. That is, we still use all of the data but we represent the spatial structure through a dimension reduction. So, again, in implementing the reduction, we need to design the knots. Consideration of this issue forms the balance of the article. To evaluate the performance of this class of models, we conduct a simulation study as well as analysis of a real data set regarding the quality of underground mineral water of a large area in Golestan province, Iran. |
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Keywords: Inference Bayesian, MCMC Algorithm, Spatio-Temporal data, knot set, low-rank models. |
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Type of Study: Applicable |
Subject:
Special Received: 2017/03/13 | Accepted: 2017/12/16 | Published: 2017/12/16
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