UCSC-SOE-10-15: Bayesian Inference for Sensitivity Analysis of Computer Simulators, with an Application to Radiative Transfer Models

Marian Farah, Athanasios Kottas
04/23/2010 09:00 AM
Applied Mathematics & Statistics
Computer simulators are used in science and technology to model
physical processes or the behavior of real-world systems. Sensitivity analysis
provides a useful tool for quantifying the impact of uncertainty in the computer
simulator inputs on the computed output. We focus on global sensitivity analysis, which quantifies output uncertainty as all the inputs vary continuously over the input space.
The influence of each input and how uncertainty in the output is apportioned amongst the inputs are determined by calculating the main effects and sensitivity indices of the computer simulator inputs. Typically, these quantities are computed using Monte Carlo
methods, which require a large number of computer simulator runs, making the
calculations infeasible if the simulator is computationally expensive. Bayesian methods have been used to tackle sensitivity analysis of computationally expensive simulators through building a statistical emulator for the computer simulator output, typically, based on a Gaussian process prior for the simulator output function. In this work, we develop an approach for integrating global sensitivity analysis tools and extending semi-Bayesian approaches to a fully Bayesian methodology. The approach is utilized to carry out sensitivity analysis of the Leaf-Canopy Model, a radiative transfer model that simulates the interaction of sunlight with vegetation.