Bayesian Inference for Diffusions with Low-Frequency Observations

Most frequentist techniques for parameter estimation in diffusion processes struggle when inter-observation times are large, which is often the case in life sciences. This chapter introduces Bayesian inference methods which estimate missing data such that the union of missing values and observations forms a high-frequency dataset. This facilitates approximation of the likelihood function and hence enables parametric inference even for large inter-observation times. Moreover, the techniques are suitable for irregularly spaced observation intervals, multivariate diffusions with possibly latent components and for observations that are subject to measurement error. This chapter brings together approaches from different authors, explains convergence problems that arise in standard algorithms, and suggests a new sampling scheme which fixes corresponding limitations of existing methods. The universal applicability of this method is proven. The contents of this chapter address both practicioners who wish to implement the estimation schemes and theoreticians who are interested in convergence proofs.