Reversible jump MCMC for nonparametric drift estimation for diffusion processes

Abstract

In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional diffusion. The drift is modeled by a scaled linear combination of basis functions with a Gaussian prior on the coefficients. The scaling parameter is equipped with a partially conjugate prior. The number of basis function in the drift is equipped with a prior distribution as well. For continuous data, a reversible jump Markov chain algorithm enables the exploration of the posterior over models of varying dimension. Subsequently, it is explained how data-augmentation can be used to extend the algorithm to deal with diffusions observed discretely in time. Some examples illustrate that the method can give satisfactory results. In these examples a comparison is made with another existing method as well.

References in corpus (2)

• MCMC using Hamiltonian dynamics
• Consistent nonparametric Bayesian inference for discretely observed scalar diffusions

Cited by in corpus (16)

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• Continuous-discrete smoothing of diffusions
• Non-parametric Bayesian drift estimation for stochastic differential equations
• Consistency of Bayesian nonparametric inference for discretely observed jump diffusions
• Adaptive nonparametric drift estimation for diffusion processes using Faber-Schauder expansions
• Beyond trans-dimensional RJMCMC with a case study in impulsive data modeling
• Consistent non-parametric Bayesian estimation for a time-inhomogeneous Brownian motion
• Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient
• Nonparametric Bayesian volatility estimation
• Full adaptation to smoothness using randomly truncated series priors with Gaussian coefficients and inverse gamma scaling
• Nonparametric Bayesian methods for one-dimensional diffusion models
• Posterior Consistency via Precision Operators for Bayesian Nonparametric Drift Estimation in SDEs
• The nonparametric LAN expansion for discretely observed diffusions