Bayesian inference of scaled versus fractional Brownian motion

Parameter Estimation: The Proper Way to Use Bayesian Posterior Processes with Brownian Noise

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior distribution processes is, in general, not equal to the posterior distribution process of the mentioned Brownian motion with the unknown drift. Instead, it is equal to the posterior distribution process associated with a Brownian motion with the same unknown drift and a different standard deviation coefficient. The difference between the two standard deviation coeffi…

关于分数布朗运动漂移的贝叶斯序列检验

A Bayesian sequential test for the drift of a fractional Brownian motion

本文提出了一种基于贝叶斯方法的序列检验，用于检测分数布朗运动的漂移方向，通过将问题转化为标准布朗运动的最优停止问题，解决了漂移正负的假设检验问题。

Bayesian Parameter Inference for Partially Observed SDEs driven by Fractional Brownian Motion

In this paper we consider Bayesian parameter inference for partially observed fractional Brownian motion (fBM) models. The approach we follow is to time-discretize the hidden process and then to design Markov chain Monte Carlo (MCMC) algorithms to sample from the posterior density on the parameters given data. We rely on a novel representation of the time discretization, which seeks to sample from an approximation of the posterior and then corrects via importance sampling; the approximation reduces the time (in terms of total observation time T) by O(T). This method is extended by using a mult…

Bias-correction of the maximum likelihood estimator for the $α$-Brownian bridge

The $α$-Brownian bridge, or scaled Brownian bridge, is a generalization of the Brownian bridge with a scaling parameter that determines how strong the force that pulls the process back to 0 is. The bias of the maximum likelihood estimator of the parameter $α$ is derived and a bias-correction that improves the estimator substantially is proposed. The properties of the bias-corrected estimator and four Bayesian estimators based on non-informative priors are evaluated in a simulation study.