Stochastic Variational Bayes Estimation for Multi-Site Daily Precipitation Data

• Activity Number: 169 - Advanced Bayesian Topics (Part 2)
• Type: Contributed
• Date/Time: Tuesday, August 10, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Reetam Majumder* and Nagaraj K Neerchal and Amita Mehta and Matthias K Gobbert
• Companies: University of Maryland, Baltimore County and University of Maryland, Baltimore County and University of Maryland, Baltimore County and University of Maryland, Baltimore County
• Keywords: Variational Bayes; Spatio-Temoral Modeling; Hidden Markov Models; Stochastic Optimization; Gaussian Copula; Semi-continuous Mixture Modeling

Abstract

Hidden Markov models (HMM) are a common approach to precipitation modeling, wherein multi-site daily precipitation is assumed to be driven by a latent first-order Markov chain representing underlying weather states. Daily precipitation is specified as a semi-continuous distribution with a point mass at zero for no rainfall and a mixture of Exponential distributions for positive rainfall. We implement variational Bayes as an alternative to the conventionally used Baum-Welch algorithm for parameter estimation in HMMs. Stochastic gradient ascent with block bootstrapping is used to optimize the variational posterior, and a Gaussian copula is constructed to capture the spatial correlations between locations. We test this model using daily precipitation data for the Chesapeake Bay watershed, a large estuarine ecosystem in Eastern USA, for the rainy season months of July to September. Remote sensing data from GPM-IMERG is used for our study, which covers the watershed with 1927 grid points at a 0.1° x 0.1° resolution. Synthetic data generated from the fitted model is able to replicate key spatial and temporal characteristics of historical precipitation data.