In this paper, we consider the problem of predicting a large scale spatial field using successive noisy measurements obtained by mobile sensing agents. The physical spatial field of interest is discretized and modeled by a Gaussian Markov random field (GMRF) with uncertain hyperparameters. From a Bayesian perspective, we design a sequential prediction algorithm to exactly compute the predictive inference of the random field. The main advantages of the proposed algorithm are: (1) the computational efficiency due to the sparse structure of the precision matrix, and (2) the scalability as the number of measurements increases. Thus, the prediction algorithm correctly takes into account the uncertainty in hyperparameters in a Bayesian way and is also scalable to be usable for mobile sensor networks with limited resources. We also present a distributed version of the prediction algorithm for a special case. An adaptive sampling strategy is presented for mobile sensing agents to find the most informative locations in taking future measurements in order to minimize the prediction error and the uncertainty in hyperparameters simultaneously. The effectiveness of the proposed algorithms is illustrated by numerical experiments.
Bibliographical noteFunding Information:
Tapabrata Maiti is a world class statistician, a fellow of the American Statistical Association and the Institute of Mathematical Statistics. He has published research articles in top tier statistics journals such as the journal of the American Statistical Association, Annals of Statistics, the Journal of the Royal Statistical Society, Series B, Biometrika, Biometrics, etc. He has also published research articles in engineering, economics, genetics, medicine and social sciences. His research has been supported by the National Science Foundation and National Institutes of Health. He presented his work in numerous national and international meetings and in academic departments. Prof. Maiti served in editorial board of several statistics journals including journal of the American Statistical Association and journal of Agricultural, Environmental and Biological Statistics. He has also served on several professional committees. Currently, he is a professor and the graduate director in the department of statistics and probability, Michigan State University. Prior to MSU, he was a tenured faculty member in the department of statistics, Iowa State University. Professor Maiti has supervised several Ph.D. students and regularly teaches statistics and non-stat major graduate students.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Electrical and Electronic Engineering