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Activity Number:
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164
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Type:
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Contributed
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Date/Time:
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Monday, August 3, 2009 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #305145 |
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Title:
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A Derivative-Free Approach to Approximation of Computationally Expensive Posterior Densities
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Author(s):
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Nikolay Bliznyuk*+
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Companies:
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Harvard School of Public Health
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Address:
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Department of Biostatistics, , ,
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Keywords:
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Bayesian calibration ; computer experiments ; groundwater modeling ; inverse problems ; Markov Chain Monte Carlo
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Abstract:
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Bayesian inference using MCMC is computationally prohibitive when the posterior density $\pi$ is expensive to evaluate. We develop a derivative-free algorithm GRIMA to approximate the logarithm of $\pi$ using interpolation by radial basis functions over a high probability density (HPD) region of $\pi$ that is not known in advance. GRIMA iterates sequential knot selection over the estimated HPD region of $\pi$ to refine the surrogate posterior and re-estimation of the HPD region by MCMC using the updated surrogate density. Sampling of the approximation to $\pi$ is cheap and allows one to reduce the cost of MCMC dramatically over the naive approach. We use GRIMA for Bayesian inference in a computationally intensive nonlinear regression model for real measured streamflow data in the Town Brook watershed. However, GRIMA is applicable to problems other than nonlinear regression.
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