TY - JOUR
T1 - Bayesian estimation of incompletely observed diffusions
AU - van der Meulen, F.
AU - Schauer, M.
PY - 2018/7/4
Y1 - 2018/7/4
N2 - We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on an unknown parameter. A data-augmentation algorithm for drawing from the posterior distribution is presented which is based on simulating diffusion bridges conditional on a noisy incomplete observation at an intermediate time. The dynamics of such filtered bridges are derived and it is shown how these can be simulated using a generalised version of the guided proposals introduced in Schauer, Van der Meulen and Van Zanten (2017, Bernoulli 23(4A)).
AB - We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on an unknown parameter. A data-augmentation algorithm for drawing from the posterior distribution is presented which is based on simulating diffusion bridges conditional on a noisy incomplete observation at an intermediate time. The dynamics of such filtered bridges are derived and it is shown how these can be simulated using a generalised version of the guided proposals introduced in Schauer, Van der Meulen and Van Zanten (2017, Bernoulli 23(4A)).
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85030709463&partnerID=MN8TOARS
U2 - 10.1080/17442508.2017.1381097
DO - 10.1080/17442508.2017.1381097
M3 - Article
SN - 1744-2508
VL - 90
SP - 641
EP - 662
JO - Stochastics : An International Journal of Probability and Stochastic Processes
JF - Stochastics : An International Journal of Probability and Stochastic Processes
IS - 5
ER -