Premium
Statistical properties of the state obtained by solving a nonlinear multivariate inverse problem
Author(s) -
Cressie Noel,
Wang Rui
Publication year - 2012
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.1946
Subject(s) - state vector , state (computer science) , inverse problem , multivariate statistics , state space , mathematics , multivariate normal distribution , nonlinear system , distribution (mathematics) , statistical model , statistical physics , mathematical optimization , statistics , algorithm , mathematical analysis , physics , classical mechanics , quantum mechanics
This article takes a statistical approach to solving a multivariate state‐space problem where many data are nonlinearly related to a state vector. The state is unknown and to be predicted, but the problem can be ill posed. A state‐space model quantifies the variability of the physical process (state equation) and of the measurements related to the process (measurement equation). The resulting posterior distribution is then maximized, yielding the predicted state vector. Statistical properties of the predicted state vector, in particular its first two moments with respect to the joint distribution, are approximated using the delta method. These are then applied to the problem of retrieving, from satellite data, a profile of CO 2 values in a column of the atmosphere. Copyright © 2012 John Wiley & Sons, Ltd.