The GIGG-EnKF: ensemble Kalman filtering for highly skewed non-negative uncertainty distributions
Craig H Bishop
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY | WILEY | Published : 2016
Observations and predictions of near-zero non-negative variables such as aerosol, water vapour, cloud, precipitation and plankton concentrations have uncertainty distributions that are skewed and better approximated by gamma and inverse-gamma probability distribution functions (pdfs) than Gaussian pdfs. Current Ensemble Kalman Filters (EnKFs) yield suboptimal state estimates for these variables. Here, we introduce a variation on the EnKF that accurately solves Bayes' theorem in univariate cases where the prior forecasts and error-prone observations given truth come in (gamma, inverse-gamma) or (inverse-gamma, gamma) or (Gaussian, Gaussian) distribution pairs. Since its multivariate extension..View full abstract
Awarded by Office of Naval Research
This work was inspired, in part, by conversations with Derek Posselt and Daniel Hodyss on qualitative differences between the posterior distributions delivered by EnKFs and those of Monte-Carlo-Markov-Chains. The author gratefully acknowledges financial support from the Office of Naval Research, Grant N0001413WX00008.