Scientific Computing with Ordinary Differential Equations
Scientific Computing with Ordinary Differential Equations
Deterministic Global Optimization in Nonlinear Optimal Control Problems
Journal of Global Optimization
On population-based simulation for static inference
Statistics and Computing
Gaussian process modelling of latent chemical species
Bioinformatics
Bioinformatics
Monte Carlo Strategies in Scientific Computing
Monte Carlo Strategies in Scientific Computing
Estimating Bayes factors via thermodynamic integration and population MCMC
Computational Statistics & Data Analysis
Statistics and Computing
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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.