Hierarchical Models for the Marine Sciences: Analyses of Climate Variability and Fish Abundance

• Activity Number: 163
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ricardo Lemos*+ and Bruno Sanso
• Companies: NOAA/NMFS Environmental Research Division and University of California at Santa Cruz
• Keywords: Hierarchical Models ; Bayesian approach ; Dinamic Linear Models ; Discrete Process Convolutions ; Parallel computing ; Spatiotemporal data analysis

Abstract

The motivation of this work is the construction of parsimonious models for the marine sciences, making use of available data and understanding of underlying mechanisms. Hierarchical Bayesian methods (HBMs) permit the construction of layered representations of observations, processes and parameters. In HBMs, uncertainty is accommodated explicitly, through the definition of prior distributions for parameters and through the inclusion of error terms. Because model fitting takes place in a single step, estimation uncertainty is properly propagated at all levels. Markov chain Monte Carlo and goodness-of-fit methods are presented. The approach described relies mostly on Discrete Process Convolutions (DPCs) and Dynamic Linear Models (DLMs). Owing to a convolution kernel designed in this work, DPCs are shown to produce adequate spatial interpolations, capturing location-dependent anisotropy and smoothness. DLMs, in turn, allow the breakdown of time-series into multiple components: trends, seasonal cycles and transient fluctuations. Since HBMs can become comprehensive, effort is made to develop efficient algorithms for multiple processing. Large dataset problems are provided as examples.