Smooth functional tempering for nonlinear differential equation models |
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Authors: | David Campbell Russell J Steele |
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Institution: | 1. Department of Statistics and Actuarial Science, Simon Fraser University, 13450 102nd avenue, Surrey, BC, Canada, V3T 0A3 2. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Ouest, Montreal, QC, Canada, H3A 2K6
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Abstract: | Differential equations are used in modeling diverse system behaviors in a wide variety of sciences. Methods for estimating
the differential equation parameters traditionally depend on the inclusion of initial system states and numerically solving
the equations. This paper presents Smooth Functional Tempering, a new population Markov Chain Monte Carlo approach for posterior
estimation of parameters. The proposed method borrows insights from parallel tempering and model based smoothing to define
a sequence of approximations to the posterior. The tempered approximations depend on relaxations of the solution to the differential
equation model, reducing the need for estimating the initial system states and obtaining a numerical differential equation
solution. Rather than tempering via approximations to the posterior that are more heavily rooted in the prior, this new method
tempers towards data features. Using our proposed approach, we observed faster convergence and robustness to both initial
values and prior distributions that do not reflect the features of the data. Two variations of the method are proposed and
their performance is examined through simulation studies and a real application to the chemical reaction dynamics of producing
nylon. |
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Keywords: | |
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