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We develop a statistical approach for characterizing uncertainty in predictions that are made with the aid of a computer simulation model. Typically, the computer simulation code models a physical system and requires a set of inputs – some known and specified, others unknown. A limited amount of field data from the true physical system are available to(More)
The Bayesian approach allows one to easily quantify uncertainty, at least in theory. In practice, however, MCMC can be computationally expensive, particularly in complicated inverse problems. Here we present methodology for improving the speed and efficiency of an MCMC analysis by combining runs on different scales. By using a coarser scale, the chain can(More)
Spatial and spatio-temporal processes are often described with a Gaussian process model. This model can be represented as a convolution of a white noise process and a smoothing kernel. We expand upon this model by considering convolutions of non-iid background processes. We highlight two particular models based on convolutions of Markov random fields and of(More)
Gaussian processes (GP) have proven to be useful and versatile stochastic models in a wide variety of applications including computer experiments, environmental monitoring, hydrology, and climate modeling. A GP model is determined by its mean and covariance functions. In most cases, the mean is specified to be a constant, or some other simple linear(More)
Due to modern advances in computing power, the use of increasingly complex models has become practical. One class of large models that often relies on numerical techniques for parameter estimation is multiresolution models. Unfortunately, numerical maximization and sampling techniques used to estimate parameters in such complex models often explore the(More)
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