Smooth functional tempering for nonlinear differential equation models

摘要: Differential equations are used in modeling diverse system behaviors a wide variety of sciences. Methods for estimating the differential equation parameters traditionally depend on inclusion initial states and numerically solving equations. This paper presents Smooth Functional Tempering, new population Markov Chain Monte Carlo approach posterior estimation parameters. The proposed method borrows insights from parallel tempering model based smoothing to define sequence approximations posterior. tempered relaxations solution model, reducing need obtaining numerical solution. Rather than via that more heavily rooted prior, this tempers towards data features. Using our approach, we observed faster convergence robustness both values prior distributions do not reflect features data. Two variations their performance is examined through simulation studies real application chemical reaction dynamics producing nylon.