Bayesian Latent Variable Co-kriging Model in Remote Sensing for Observations with Quality Flagged

Remote sensing data products often include quality flags that inform users whether the associated observations are of good, acceptable or unreliable qualities. However, such information on data fidelity is not considered in remote sensing data analyses. Motivated by observations from the Atmospheric Infrared Sounder (AIRS) instrument on board NASA's Aqua satellite, we propose a latent variable co-kriging model with separable Gaussian processes to analyze large quality-flagged remote sensing data sets together with their associated quality information. We augment the posterior distribution by an imputation mechanism to decompose large covariance matrices into separate computationally efficient components taking advantage of their input structure. Within the augmented posterior, we develop a Markov chain Monte Carlo (MCMC) procedure that mostly consists of direct simulations from conditional distributions. In addition, we propose a computationally efficient recursive prediction procedure. We apply the proposed method to air temperature data from the AIRS instrument. We show that incorporating quality flag information in our proposed model substantially improves the prediction performance compared to models that do not account for quality flags.