Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
On sequential Monte Carlo sampling methods for Bayesian filtering
Statistics and Computing
Bayesian sequential inference for nonlinear multivariate diffusions
Statistics and Computing
Particle filters for state-space models with the presence ofunknown static parameters
IEEE Transactions on Signal Processing
Bayesian inference for a discretely observed stochastic kinetic model
Statistics and Computing
Computational Statistics & Data Analysis
Estimating Bayes factors via thermodynamic integration and population MCMC
Computational Statistics & Data Analysis
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
Computational Statistics & Data Analysis
Slow convergence of sequences of linear operators II: Arbitrarily slow convergence
Journal of Approximation Theory
A regularized bridge sampler for sparsely sampled diffusions
Statistics and Computing
Rate estimation in partially observed Markov jump processes with measurement errors
Statistics and Computing
Inference for non-linear diffusions and jump-diffusions: a Monte Carlo EM approach
ACMIN'12 Proceedings of the 14th international conference on Automatic Control, Modelling & Simulation, and Proceedings of the 11th international conference on Microelectronics, Nanoelectronics, Optoelectronics
Moment closure based parameter inference of stochastic kinetic models
Statistics and Computing
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Diffusion processes governed by stochastic differential equations (SDEs) are a well-established tool for modelling continuous time data from a wide range of areas. Consequently, techniques have been developed to estimate diffusion parameters from partial and discrete observations. Likelihood-based inference can be problematic as closed form transition densities are rarely available. One widely used solution involves the introduction of latent data points between every pair of observations to allow a Euler-Maruyama approximation of the true transition densities to become accurate. In recent literature, Markov chain Monte Carlo (MCMC) methods have been used to sample the posterior distribution of latent data and model parameters; however, naive schemes suffer from a mixing problem that worsens with the degree of augmentation. A global MCMC scheme that can be applied to a large class of diffusions and whose performance is not adversely affected by the number of latent values is therefore explored. The methodology is illustrated by estimating parameters governing an auto-regulatory gene network, using partial and discrete data that are subject to measurement error.