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(2015), xx, x, pp . 1–19 Bayesian inference for partially observed SDEs driven by fractional Brownian motion BY A. BESKOS Department of Statistical Science, University College London, 5 1-19 Torrington Place, London WC1E 7HB, U.K. 1 0 a.beskos@ucl.ac.uk 2 r J. DUREAU a M Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, U.K. 4 dureau.joseph@ 2 ] AND K. KALOGEROPOULOS E Department of Statistics, London School of Economics, M Houghton Street, London WC2A 2AE, U.K. . t k.kalogeropoulos@lse.ac.uk a t s [ SUMMARY 5 We consider continuous-time diffusion models driven by fractional Brownian motion. Obser- v vations are assumed to possess a non-trivial likelihood given the latent path. Due to the non- 8 3 Markovianity and high dimensionality of the latent paths, estimating posterior expectations is 2 computationally challenging. We present a reparameterization framework based on the Davies 0 and Harte method for sampling stationary Gaussian processes and use it to construct a Markov . 7 chain Monte Carlo algorithm that allows computationally efficient Bayesian inference. The algo- 0 rithm is based on a version of