Quantifying Model Error in Posterior Distributions

• Activity Number: 195
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Staci White*+ and Radu Herbei
• Companies: The Ohio State University and The Ohio State University
• Keywords: PDE ; model error ; pre-processing

Abstract

We study Bayesian hierarchical models in environmental applications where likelihood calculations frequently involve a solution to a partial differential equation (PDE). Analytical solutions to such PDEs are rarely available in closed form. Thus, a numerical solver is used which requires a user-specified model-grid. However, the data are collected at locations that do not coincide with grid points. Common practice is to process the data by smoothing or interpolating it to align with the model-grid. In this work, we study the discrepancy between posterior distributions obtained by using actual data versus pre-processed data. We quantify the model error in the resulting posterior distributions using the Hellinger distance. Our results are illustrated with hydrographic data from the South Atlantic Ocean collected during the WOCE experiment.