Joint segmentation of multivariate astronomical time series : bayesian sampling with a hierarchical model

Astronomy and other sciences often face the problem of detecting and characterizing structure in two or more related time series. This paper approaches such problems using Bayesian priors to represent relationships between signals with various degrees of certainty, and not just rigid constraints. The segmentation is conducted by using a hierarchical Bayesian approach to a piecewise constant Poisson rate model. A Gibbs sampling strategy allows joint estimation of the unknown parameters and hyperparameters. Results obtained with synthetic and real photon counting data illustrate the performance of the proposed algorithm

Bayesian detection of piecewise linear trends in replicated time-series with application to growth data modelling

We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as a piecewise linear function of time with an unknown number of change-points. We develop a Bayesian approach to infer the joint posterior distribution of the number and position of change-points as well as the unknown mean parameters. A-priori, the proposed model uses an overfitting number of mean parameters but, conditionally on a set of change-points, only a subset of them influences the likelihood. An exponentially decreasing prior distribution on the number of change-points gives rise to a posterior distribution concentrating on sparse representations of the underlying sequence. A Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampler is constructed for approximating the posterior distribution. Our method is benchmarked using simulated data and is applied to uncover differences in the dynamics of fungal growth from imaging time course data collected from different strains. The source code is available on CRAN.Comment: Accepted to International Journal of Biostatistic

Exact asymptotic distribution of change-point mle for change in the mean of Gaussian sequences

We derive exact computable expressions for the asymptotic distribution of the change-point mle when a change in the mean occurred at an unknown point of a sequence of time-ordered independent Gaussian random variables. The derivation, which assumes that nuisance parameters such as the amount of change and variance are known, is based on ladder heights of Gaussian random walks hitting the half-line. We then show that the exact distribution easily extends to the distribution of the change-point mle when a change occurs in the mean vector of a multivariate Gaussian process. We perform simulations to examine the accuracy of the derived distribution when nuisance parameters have to be estimated as well as robustness of the derived distribution to deviations from Gaussianity. Through simulations, we also compare it with the well-known conditional distribution of the mle, which may be interpreted as a Bayesian solution to the change-point problem. Finally, we apply the derived methodology to monthly averages of water discharges of the Nacetinsky creek, Germany.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS294 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

The application of Bayesian change point detection in UAV fuel systems

AbstractA significant amount of research has been undertaken in statistics to develop and implement various change point detection techniques for different industrial applications. One of the successful change point detection techniques is Bayesian approach because of its strength to cope with uncertainties in the recorded data. The Bayesian Change Point (BCP) detection technique has the ability to overcome the uncertainty in estimating the number and location of change point due to its probabilistic theory. In this paper we implement the BCP detection technique to a laboratory based fuel rig system to detect the change in the pre-valve pressure signal due to a failure in the valve. The laboratory test-bed represents a Unmanned Aerial Vehicle (UAV) fuel system and its associated electrical power supply, control system and sensing capabilities. It is specifically designed in order to replicate a number of component degradation faults with high accuracy and repeatability so that it can produce benchmark datasets to demonstrate and assess the efficiency of the BCP algorithm. Simulation shows satisfactory results of implementing the proposed BCP approach. However, the computational complexity, and the high sensitivity due to the prior distribution on the number and location of the change points are the main disadvantages of the BCP approac