The Computational Cost of Blocking for Sampling Discretely Observed Diffusions

Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

We introduce verifiable criteria for weak posterior consistency of Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient in arbitrary dimension. The criteria are expressed in terms of coefficients of the SDEs describing the process, and do not depend on intractable quantities such as transition densities. In particular, we are able to show that posterior consisten...

Discretely Observed Diffusions: Approximation of the Continuous-time Score Function

Discretely Observed Diffusions: Approximation of the Continuous-time Score Function

We discuss parameter estimation for discretely observed, ergodic diffusion processes where the diffusion coefficient does not depend on the parameter. We propose using an approximation of the continuous-time score function as an estimating function. The estimating function can be expressed in simple terms through the drift and the diffusion coefficient and is thus easy to calculate. Simulation ...

Consistent nonparametric Bayesian inference for discretely observed scalar diffusions

FRANK VAN DER MEULEN1 and HARRY VAN ZANTEN2 1Delft Institute of Applied Mathematics (DIAM), Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands. E-mail: [email protected] 2Department of Mathematics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: j....

Estimation for Discretely Observed Diffusions using Transform Functions

This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions...