Reversible jump MCMC for nonparametric drift estimation for diffusion processes

@article{Meulen2014ReversibleJM,
  title={Reversible jump MCMC for nonparametric drift estimation for diffusion processes},
  author={Frank van der Meulen and Moritz Schauer and Harry van Zanten},
  journal={Comput. Stat. Data Anal.},
  year={2014},
  volume={71},
  pages={615-632}
}

Bayesian inference and model selection for multi-dimensional diffusion process models with non-parametric drift and constant diffusivity

TLDR
With the goal of model improvement in mind, this work describes how outlier removal and systematic sub-sampling of the data can be beneficial and implements the Bayesian discrepancy p-value to complement the inference methodology.

Nonparametric Bayesian Estimation of a Hölder Continuous Diffusion Coefficient

We consider a nonparametric Bayesian approach to estimate the diffusion coefficient of a stochastic differential equation given discrete time observations over a fixed time interval. As a prior on

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

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

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

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

Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals

TLDR
A general framework to deal with estimation of parameters of a diffusion based on discrete time observations that does not rely on discretisation is presented and a random-walk type Metropolis-Hastings sampler for updating diffusion bridges is defined.

Nonparametric estimation of diffusions: a differential equations approach

We consider estimation of scalar functions that determine the dynamics of diffusion processes. It has been recently shown that nonparametric maximum likelihood estimation is ill-posed in this

Bayesian semi-parametric inference for diffusion processes using splines

We introduce a semi-parametric method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions

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

TLDR
A Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data is studied and the rate at which the posterior contracts around the true drift function is bound.

Consistency of Bayesian nonparametric inference for discretely observed jump diffusions

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

Continuous-discrete smoothing of diffusions

TLDR
A novel Markov Chain Monte Carlo algorithm is derived to sample from the exact smoothing distribution of a multivariate diffusion process, called the Backward Filtering Forward Guiding (BFFG) algorithm, which is extended to include parameter estimation.

References

SHOWING 1-10 OF 29 REFERENCES

On inference for partially observed nonlinear diffusion models using the Metropolis–Hastings algorithm

TLDR
A new Markov chain Monte Carlo approach to Bayesian analysis of discretely observed diffusion processes and shows that, because of full dependence between the missing paths and the volatility of the diffusion, the rate of convergence of basic algorithms can be arbitrarily slow if the amount of the augmentation is large.

Nonparametric estimation of diffusions: a differential equations approach

We consider estimation of scalar functions that determine the dynamics of diffusion processes. It has been recently shown that nonparametric maximum likelihood estimation is ill-posed in this

Reversible jump Markov chain Monte Carlo computation and Bayesian model determination

Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed

Trans-dimensional Markov chain Monte Carlo

Summary In the context of sample-based computation of Bayesian posterior distributions in complex stochastic systems, this chapter discusses some of the uses for a Markov chain with a prescribed

On the Relationship Between Markov chain Monte Carlo Methods for Model Uncertainty

This article considers Markov chain computational methods for incorporating uncertainty about the dimension of a parameter when performing inference within a Bayesian setting. A general class of

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

TLDR
This work considers approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non‐Gaussian response variables and can directly compute very accurate approximations to the posterior marginals.

Retrospective exact simulation of diffusion sample paths with applications

TLDR
An algorithm for exact simulation of a class of Ito's diffusions and a method that exploits the properties of the algorithm to carry out inference on discretely observed diffusions without resorting to any kind of approximation apart from the Monte Carlo error is described.

Diffusions, Markov processes, and martingales

This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first,

Handbook of Markov Chain Monte Carlo

TLDR
A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data and its applications in environmental epidemiology, educational research, and fisheries science are studied.