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We consider the problem of statistical inference for a class ofpartially-observed diffusion processes, with discretely-observed data andfinite-dimensional parameters. We construct unbiased estimators of the scorefunction, i.e. the gradient of the log-likelihood function with respect toparameters, with no time-discretization bias. These estimators can bestraightforwardly employed within stochastic gradient methods to performmaximum likelihood estimation or Bayesian inference. As our proposedmethodology only requires access to a time-discretization scheme such as theEuler-Maruyama method, it is applicable to a wide class of diffusion processesand observation models. Our approach is based on a representation of the scoreas a smoothing expectation using Girsanov theorem, and a novel adaptation ofthe randomization schemes developed in Mcleish [2011], Rhee and Glynn [2015],Jacob et al. [2020a]. This allows one to remove the time-discretization biasand burn-in bias when computing smoothing expectations using the conditionalparticle filter of Andrieu et al. [2010]. Central to our approach is thedevelopment of new couplings of multiple conditional particle filters. We proveunder assumptions that our estimators are unbiased and have finite variance.The methodology is illustrated on several challenging applications frompopulation ecology and neuroscience.

On Unbiased Score Estimation for Partially Observed Diffusions