A0427
Title: Heteroskedastic hidden dynamic geostatistical models for environmental data
Authors: Jacopo Rodeschini - University of Bergamo (Italy) [presenting]
Alessandro Fusta Moro - University of Bergamo (Italy)
Andrea Moricoli - University of Bergamo (Italy)
Alessandro Fasso - University of Bergamo (Italy)
Abstract: A common framework for studying spatiotemporal processes is the state space model (SSM) and the related Kalman filter technique. In this context, a well-established multivariate spatiotemporal model is the hidden dynamic geostatistical model (HDGM), which is an SSM suitable for complex environmental processes. The observation variability is modelled by the measurement equation, which is essentially given by a regression component, a stochastic latent process, and an error term. The spatiotemporal correlation is modelled by the latent equation through a Markovian process, with the innovation term being a zero-mean Gaussian process with a spatial covariance function. In environmental studies, addressing heteroskedasticity is crucial for accurate inference. In spatiotemporal models, heteroskedasticity can relate to time, space, data heterogeneity, or a combination thereof. Data heterogeneity often occurs in data fusion problems, where data come from various sensors or processes. Two heteroskedastic extensions of the HDGM are compared, featuring time-varying error variance. The first method treats error variance as a nuisance parameter, employing a flexible, unstructured, time-varying error variance. The second method models error variance as a linear combination of time-based basis functions. Both methods estimate model parameters using the expectation-maximization algorithm.
