Ensemble-based characterization of uncertain environmental features

This paper considers the characterization of uncertain spatial features that cannot be observed directly but must be inferred from noisy measurements. Examples of interest in environmental applications include rainfall patterns, solute plumes, and geological features. We formulate the characterization process as a Bayesian sampling problem and solve it with a non-parametric version of importance sampling. All images are concisely described with a small number of image attributes. These are derived from a multidimensional scaling procedure that maps high dimensional vectors of image pixel values to much lower dimensional vectors of attribute values. The importance sampling procedure is carried out entirely in terms of attribute values. Posterior attribute probabilities are derived from non-parametric estimates of the attribute likelihood and proposal density. The likelihood is inferred from an archive of noisy operational images that are paired with more accurate ground truth images. Proposal samples are generated from a non-stationary multi-point statistical algorithm that uses training images to convey distinctive feature characteristics. To illustrate concepts we carry out a virtual experiment that identifies rainy areas on the Earth’s surface from either one or two remote sensing measurements. The two sensor case illustrates the method’s ability to merge measurements with different error properties. In both cases, the importance sampling procedure is able to identify the proposals that most closely resemble a specified true image.