More Efficient Sampling for Bayesian Calibration of Computationally Expensive Hydrologic and Environmental Simulation Models

Xie, Hua

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Description

Title

More Efficient Sampling for Bayesian Calibration of Computationally Expensive Hydrologic and Environmental Simulation Models

Author(s)

Xie, Hua

Issue Date

2009

Doctoral Committee Chair(s)

Eheart, J. Wayland

Department of Study

Civil Engineering

Discipline

Environmental Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

Engineering, Civil

Abstract

• In recent years, interest in Bayesian calibration of hydrologic and environmental simulation (HE) models has been growing. The Bayesian approach allows for making statistical inference on unknown parameters and has proved to be an effective method to treat the estimation uncertainty arising from the calibration requirements of these models.
• In Bayesian calibration, the posterior density function contains all the information generated in the calibration, and extra effort has to be made to determine the summary quantities of interest. The posterior density function may have complicated functional form and is rarely analytically tractable. In most cases, it is necessary to rely on the Monte Carlo method, or samples drawn from the posterior distribution to extract useful information from the posterior density. Sampling a posterior distribution requires a large number of evaluations of the posterior density functions or the HE models. The computationally intensive nature of Monte Carlo simulation often limits its use and even the applicability of Bayesian calibration approach, especially when the HE models are computationally expensive.
• In this dissertation, a computing strategy is proposed to improve the computational efficiency in the Bayesian calibration for computationally demanding HE models. The basic idea is to seek more efficient utilization of the information on the response surface of the posterior density function generated in a costly run of simulation models by using multiple evaluations of the posterior density in the less computationally expensive subspace of error model parameters. Here, the error model parameters refer to those parameters that are introduced in the calibration to characterize the statistical structure of residuals.
• A multiple-try Markov chain Monte Carlo (MCMC) algorithm is designed to implement this idea and is applied both to one of the most simple and one of the most complex HE models. The simple model is a two-parameter BOD model; the complex model is an eight-parameter version of the Soil and Water Assessment Tool (SWAT) model applied to the Upper Sangamon River Basin in east central Illinois. The MCMC has increasingly become the standard technique for Monte Carlo simulation in Bayesian calibration. The efficiency of the proposed multiple-try algorithm is first compared with the Metropolis-Hastings algorithm, a basic recipe for Monte Carlo based Bayesian computation, in the posterior sampling problem defined in the calibration of a BOD model. The proposed multiple-try algorithm shows two advantages over the Metropolis-Hastings algorithm: first, it is more robust in terms of proposal distribution setup and therefore has potential to reduce the costs at the proposal distribution tuning stage; second, it provides more accurate estimates of the summary quantities of the posterior distributions, as indicated by the mean square errors of posterior mean estimates of parameters.
• The findings from the simple BOD model calibration problem are confirmed in the Bayesian calibration of the SWAT model. The SWAT model is developed to simulate the hydrological conditions of the Upper Sangamon River Basin, and is calibrated to the discharge data collected at the outlet of the study watershed. A total of twelve parameters, including eight SWAT model parameters and four error model parameters are considered in the calibration. In the MCMC posterior sampling, it takes about 30% less time to complete the setting of the proposal distributions for the proposed algorithm than for the application of the Metropolis-Hastings algorithm. Furthermore, when the proposed multiple-try algorithm is applied, significant reductions in integrated autocorrelation times (IATs) for the four error model parameters are observed, and the standard errors of posterior mean estimates of four error model parameters are reduced by 60--70%.
• According to the results of the posterior sampling in the Bayesian calibration of the BOD and SWAT models, the proposed strategy is an effective approach for improving the efficiency of posterior sampling in the Bayesian calibration of computationally expensive HE models.

Graduation Semester

2009

Type of Resource

text

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