BibTex format

author = {Chkrebtii, OA and Campbell, DA and Calderhead, B and Girolami, MA},
doi = {10.1214/16-BA1017},
journal = {Bayesian Analysis},
pages = {1239--1267},
title = {Bayesian Solution Uncertainty Quantification for Differential Equations},
url = {},
volume = {11},
year = {2016}

RIS format (EndNote, RefMan)

AB - We explore probability modelling of discretization uncertainty for systemstates defined implicitly by ordinary or partial differential equations. Accountingfor this uncertainty can avoid posterior under-coverage when likelihoods areconstructed from a coarsely discretized approximation to system equations. A formalismis proposed for inferring a fixed but a priori unknown model trajectorythrough Bayesian updating of a prior process conditional on model information.A one-step-ahead sampling scheme for interrogating the model is described, itsconsistency and first order convergence properties are proved, and its computationalcomplexity is shown to be proportional to that of numerical explicit one-stepsolvers. Examples illustrate the flexibility of this framework to deal with a widevariety of complex and large-scale systems. Within the calibration problem, discretizationuncertainty defines a layer in the Bayesian hierarchy, and a Markovchain Monte Carlo algorithm that targets this posterior distribution is presented.This formalism is used for inference on the JAK-STAT delay differential equationmodel of protein dynamics from indirectly observed measurements. The discussionoutlines implications for the new field of probabilistic numerics.
AU - Chkrebtii,OA
AU - Campbell,DA
AU - Calderhead,B
AU - Girolami,MA
DO - 10.1214/16-BA1017
EP - 1267
PY - 2016///
SN - 1936-0975
SP - 1239
TI - Bayesian Solution Uncertainty Quantification for Differential Equations
T2 - Bayesian Analysis
UR -
UR -
UR -
VL - 11
ER -