Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/33910

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Title
Quantifying parameter uncertainty in stochastic models using the Box-Cox transformation
Author/Creator
Thyer, Mark;  Kuczera, George Alfred;  Wang, Q. J.
Institution
The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
Description
The Box–Cox transformation is widely used to transform hydrological data to make it approximately Gaussian. Bayesian evaluation of parameter uncertainty in stochastic models using the Box–Cox transformation is hindered by the fact that there is no analytical solution for the posterior distribution. However, the Markov chain Monte Carlo method known as the Metropolis algorithm can be used to simulate the posterior distribution. This method properly accounts for the nonnegativity constraint implicit in the Box–Cox transformation. Nonetheless, a case study using the AR(1) model uncovered a practical problem with the implementation of the Metropolis algorithm. The use of a multivariate Gaussian jump distribution resulted in unacceptable convergence behaviour. This was rectified by developing suitable parameter transformations for the mean and variance of the AR(1) process to remove the strong nonlinear dependencies with the Box–Cox transformation parameter. Applying this methodology to the Sydney annual rainfall data and the Burdekin River annual runoff data illustrates the efficacy of these parameter transformations and demonstrate the value of quantifying parameter uncertainty.
Relation
Journal of Hydrology Vol. 265, Issue 1-4, p. 246-257
Publisher Link
http://dx.doi.org/10.1016/S0022-1694(02)00113-0
Date
2002
Publisher
Elsevier
Keyword(s)
lag-one autoregressive models;  Markov chain Monte Carlo methods;  metropolis algorithm;  parameter uncertainty;  Box–Cox transformation
Resource Type
journal article
Identifier
http://hdl.handle.net/1959.13/33910
Identifier
ISSN:0022-1694
Reviewed
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Subject
"Journal of Hydrology"
 
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