[M-GI33] Data-driven geosciences

[MGI33-05] Spatial resolution of Bayesian sensing

*Tatsu Kuwatani¹, Hideitsu Hino², Nagata Kenji³, Takahiro Kawashima⁴, mitsuhiro toriumi¹, Masato Okada⁵ (1.Japan Agency for Marine-Earth Science and Technology, 2.The Institute of Statistical Mathematics, 3.National Institute for Materials Science, 4.Graduate University for Advanced Studies, 5.The University of Tokyo)

Keywords:Bayesian estimation, Inversion, Measurement informatics

Bayesian sensing is a general framework that uses Bayesian estimation to advance measurement and observation in order to understand the essential physics of a target system. It utilizes prior knowledge and forward models through Bayes' theorem, to enable the accurate estimation of not only the model parameters that indicate the target physical quantities, but also the hyperparameters that indicate the hidden physical parameters governing the process and structure of the target and sensing systems. This paper discusses the physical meaning and mechanism of the Bayesian sensing using the concept of resolution in spatial inversion problem. It describes that the spatial resolution of the model parameters can be spatially mapped using a resolution matrix, dened as a linear mapping from the true model parameter to the recovered model parameter. We also show that the optimal hyperparameters are obtained by internally-consistent equations between the estimated optimal and the actual hyperparameters calculated from the estimated model parameters, in terms of resolution. The obtained equations contribute toward understanding the hidden physical process and the structure of the target and sensing system in various problems, as well as the potential to reduce the computational cost.