Consistent nonparametric Bayesian inference for discretely observed scalar diffusions

DOI10.3150/11-BEJ385zbMath1259.62070arXiv1301.7567MaRDI QIDQ1940748

Harry van Zanten, Frank H. van der Meulen

Publication date: 7 March 2013

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7567

zbMATH Keywords

waveletsstochastic differential equationsBayesian nonparametricsposterior distributionposterior consistencydrift function

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Nonparametric estimation (62G05) Bayesian inference (62F15) Markov processes: estimation; hidden Markov models (62M05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (13)

Reversible jump MCMC for nonparametric drift estimation for diffusion processes ⋮ Nonparametric Bayesian methods for one-dimensional diffusion models ⋮ On Bayesian consistency for flows observed through a passive scalar ⋮ Consistency of Bayesian nonparametric inference for discretely observed jump diffusions ⋮ Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift ⋮ Flexible Bayesian inference for diffusion processesusing splines ⋮ Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions ⋮ A ridge estimator of the drift from discrete repeated observations of the solution of a stochastic differential equation ⋮ Nonparametric Bayesian drift estimation for multidimensional stochastic differential equations ⋮ Nonparametric Bayesian posterior contraction rates for scalar diffusions with high-frequency data ⋮ Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient ⋮ Bernstein-von Mises theorems for statistical inverse problems. I: Schrödinger equation ⋮ Sup-norm adaptive drift estimation for multivariate nonreversible diffusions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence rates of posterior distributions for non iid observations
• Bayesian inference for nonlinear multivariate diffusion models observed with error
• On the consistency of Bayes estimates
• Wavelets, approximation, and statistical applications
• New approaches to Bayesian consistency
• Convergence rates of posterior distributions.
• Rates of convergence of posterior distributions.
• The consistency of posterior distributions in nonparametric problems
• Posterior consistency of Dirichlet mixtures for estimating a transition density
• On inference for partially observed nonlinear diffusion models using the Metropolis-Hastings algorithm
• Exact and Computationally Efficient Likelihood-Based Estimation for Discretely Observed Diffusion Processes (with Discussion)
• Ten Lectures on Wavelets
• Foundations of Modern Probability
• Likelihood Inference for Discretely Observed Nonlinear Diffusions
• On Bayes procedures

This page was built for publication: Consistent nonparametric Bayesian inference for discretely observed scalar diffusions