Related papers: A Bayesian method for the analysis of deterministi…

Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…

We propose a two stage procedure for the estimation of the parameters of a fairly general, continuous-time stochastic volatility. An important ingredient of the proposed method is the Cuchiero-Teichmann volatility estimator, which is based…

The multivariate Ornstein-Uhlenbeck process is used in many branches of science and engineering to describe the regression of a system to its stationary mean. Here we present an $O(N)$ Bayesian method to estimate the drift and diffusion…

In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…

In recent years there have been many proposals as flexible alternatives to Gaussian based continuous time stochastic volatility models. A great deal of these models employ positive L\'evy processes. Among these are the attractive…

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behaviour. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate…

Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…

Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…

The optical light curves of many quasars show variations of tenths of a magnitude or more on time scales of months to years. This variation often cannot be described well by a simple deterministic model. We perform a Bayesian comparison of…

In this paper, we adopt a Bayesian point of view for predicting real continuous-time processes. We give two equivalent definitions of a Bayesian predictor and study some properties: admissibility, prediction sufficiency, non-unbiasedness,…

Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…

This paper addresses the issue of detecting change-points in multivariate time series. The proposed approach differs from existing counterparts by making only weak assumptions on both the change-points structure across series, and the…

We present a novel Bayesian approach to analysing multiple time-series with the aim of detecting abnormal regions. These are regions where the properties of the data change from some normal or baseline behaviour. We allow for the…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…

We consider the problem of static Bayesian inference for partially observed Levy-process models. We develop a methodology which allows one to infer static parameters and some states of the process, without a bias from the…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex…