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A new Bayesian computational approach is developed to estimate spatially varying parameters. The sparse grid collocation method is adopted to parameterize the spatial field. Based on a hierarchically structured sparse grid, a multiscale representation of the spatial field is constructed. An adaptive refinement strategy is then used for computing the spatially varying parameter. A sequential Monte Carlo (SMC) sampler is used to explore the posterior distributions defined on multiple scales. Thedoi:10.1088/0266-5611/27/10/105004 fatcat:diri7bvpdvcapjmqwaclswhxr4