B0833
Title: Block bootstrap adjustment for heteroskedastic Gaussian process
Authors: Paolo Maranzano - University of Milano-Bicocca & Fondazione Eni Enrico Mattei (Italy)
Alessandro Fasso - University of Bergamo (Italy)
Pietro Colombo - University of Glasgow (United Kingdom) [presenting]
Abstract: Environmental time series often contain gaps of varying lengths and frequencies, making it challenging to fill these gaps and quantify uncertainty during the interpolation process, particularly when dealing with input-dependent noise and heteroskedasticity. The heteroskedastic Gaussian process is a promising solution, filling gaps and providing input-dependent variance estimates. However, it requires replicate observations for each unique design location, which is not always available. The heteroskedastic Gaussian process is enhanced to address this limitation by integrating a block bootstrap adjustment for time-dependent data. This involves generating pseudo-replicates of time series with temporal gaps. The method's effectiveness is evaluated across diverse variance surfaces, noise levels, and randomized gap sequences through extensive Monte Carlo experiments. The results demonstrate that the approach is computationally efficient and flexible. User-defined parameters enable the generation of more extreme or conservative variance estimates, accommodating different modelling requirements and preferences. Overall, the extended method effectively estimates variances in environmental time-space data, even without replicates for each unique design location. Furthermore, the algorithm can be extended to handle spatial-dependent data through appropriate bootstrap adjustments.
