Entropy-based network design using hierarchical Bayesian kriging
by Yuehua Wu
Abstract: Some spatio-temporal data such as temperature, precipitation, atmospheric pressure and ozone concentration are collected from monitoring stations. However, the selection of these stations is often influenced by a variety of nonstatistical considerations. Thus it is important to evaluate if an existing station is statistically unnecessary. It is also crucial to find a location such that a new monitoring station upon it can greatly improve the data modeling. The main objective of this paper is to show how to tackle such environmental network design problems by the entropy approach. For demonstration, we consider the precipitation data from the region of Upper-Austria. To proceed, we first formulate the hierarchical spatio-temporal model to be employed based on observed precipitation data. We then fill in some missing observations such that the data has the staircase structure. After it, we estimate hyperparameters and obtain the spatial predictive distribution. Thus we are able to estimate the precipitation amount for those 445 areas located in the 18 districts of Upper-Austria in which yearly data on greenland usage are available for six years. To decide if a new gauge station needs to be added at the centers of these 445 areas or an existing station can be closed down, we solve this environmental network design problem by using the principle of maximum entropy.
Joint work with B. Jin and B. Miao.
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