# Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs

@article{Pokern2012PosteriorCV, title={Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs}, author={Yvo Pokern and Andrew M. Stuart and J. H. van Zanten}, journal={Stochastic Processes and their Applications}, year={2012}, volume={123}, pages={603-628} }

## 49 Citations

### Adaptive posterior contraction rates for empirical Bayesian drift estimation of a diffusion

- Mathematics
- 2019

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance…

### Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

- MathematicsBernoulli
- 2019

We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and…

### Nonparametric Bayesian inference of discretely observed diffusions

- Mathematics, Computer Science
- 2020

We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We…

### Bernoulli Nonparametric Bayesian posterior contraction rates for scalar diffusions with high-frequency data

- Mathematics, Computer Science
- 2018

A general theorem detailing conditions under which Bayesian posteriors will contract in L–distance around the true drift function b0 at the frequentist minimax rate is proved.

### Posterior Contraction Rates for the Bayesian Approach to Linear Ill-Posed Inverse Problems

- Mathematics
- 2013

### Approximate Bayes learning of stochastic differential equations.

- Computer Science, MathematicsPhysical review. E
- 2018

A nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector and an approximate expectation maximization algorithm to deal with the unobserved, latent dynamics between sparse observations are introduced.

### Adaptive nonparametric drift estimation for diffusion processes using Faber–Schauder expansions

- MathematicsStatistical Inference for Stochastic Processes
- 2017

We consider the problem of nonparametric estimation of the drift of a continuously observed one-dimensional diffusion with periodic drift. Motivated by computational considerations, van der Meulen et…

### Nonparametric Bayesian inference for reversible multi-dimensional diffusions

- MathematicsArXiv
- 2020

Nonparametric Bayesian modelling of reversible multi-dimensional diffusions with periodic drift is studied to prove a general posterior contraction rate theorem for the drift gradient vector field under approximation-theoretic conditions on the induced prior for the invariant measure.

### Approximate Gaussian process inference for the drift of stochastic differential equations

- Mathematics, Computer ScienceNIPS 2013
- 2013

An approximate EM algorithm is developed to deal with the unobserved, latent dynamics between observations and the posterior over states is approximated by a piecewise linearized process of the Ornstein-Uhlenbeck type.

### Reversible jump MCMC for nonparametric drift estimation for diffusion processes

- MathematicsComput. Stat. Data Anal.
- 2014

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