Bayesian model based spatiotemporal survey designs and partially observed log Gaussian Cox process

In geostatistics, the spatiotemporal design for data collection is central for accurate prediction and parameter inference. An important class of geostatistical models is log-Gaussian Cox process (LGCP) but there are no formal analyses on spatial or spatiotemporal survey designs for them. In this work, we study traditional balanced and uniform random designs in situations where analyst has prior information on intensity function of LGCP and show that the traditional balanced and random designs are not efficient in such situations. We also propose a new design sampling method, a rejection sampling design, which extends the traditional balanced and random designs by directing survey sites to locations that are a priori expected to provide most information. We compare our proposal to the traditional balanced and uniform random designs using the expected average predictive variance (APV) loss and the expected Kullback-Leibler (KL) divergence between the prior and the posterior for the LGCP intensity function in simulation experiments and in a real world case study. The APV informs about expected accuracy of a survey design in point-wise predictions and the KL-divergence measures the expected gain in information about the joint distribution of the intensity field. The case study concerns planning a survey design for analyzing larval areas of two commercially important fish stocks on Finnish coastal region. Our experiments show that the designs generated by the proposed rejection sampling method clearly outperform the traditional balanced and uniform random survey designs. Moreover, the method is easily applicable to other models in general. (C) 2019 The Author(s). Published by Elsevier B.V.