Quantifying parameter uncertainty in stochastic models using the Box-Cox transformation

Abstract

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 ..