Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Lecturer in Statistics



+44 (0)20 7594 8577b.calderhead




523Huxley BuildingSouth Kensington Campus






BibTex format

author = {Teymur, O and Calderhead, B and Lie, HC and Sullivan, T},
publisher = {Massachusetts Institute of Technology Press},
title = {Implicit probabilistic integrators for ODEs},
url = {},

RIS format (EndNote, RefMan)

AB - We introduce a family of implicit probabilistic integrators for initial value problems(IVPs), taking as a starting point the multistep Adams–Moulton method. Theimplicit construction allows for dynamic feedback from the forthcoming time-step, in contrast to previous probabilistic integrators, all of which are based onexplicit methods. We begin with a concise survey of the rapidly-expanding field ofprobabilistic ODE solvers. We then introduce our method, which builds on andadapts the work of Conrad et al. (2016) and Teymur et al. (2016), and provide arigorous proof of its well-definedness and convergence. We discuss the problem ofthe calibration of such integrators and suggest one approach. We give an illustrativeexample highlighting the effect of the use of probabilistic integrators—includingour new method—in the setting of parameter inference within an inverse problem.
AU - Teymur,O
AU - Calderhead,B
AU - Lie,HC
AU - Sullivan,T
PB - Massachusetts Institute of Technology Press
SN - 1049-5258
TI - Implicit probabilistic integrators for ODEs
UR -
ER -