Joint segmentation of wind speed and direction using a hierarchical model

The problem of detecting changes in wind speed and direction is considered. Bayesian priors, with various degrees of certainty, are used to represent relationships between the two time series. Segmentation is then conducted using a hierarchical Bayesian model that accounts for correlations between the wind speed and direction. A Gibbs sampling strategy overcomes the computational complexity of the hierarchical model and is used to estimate the unknown parameters and hyperparameters. Extensions to other statistical models are also discussed. These models allow us to study other joint segmentation problems including segmentation of wave amplitude and direction. The performance of the proposed algorithms is illustrated with results obtained with synthetic and real data

New efficient algorithms for multiple change-point detection with kernels

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, \ldots). Nonetheless, they have a high computational cost both in terms of time and memory. This makes their application difficult even for small and medium sample sizes ($n< 10^4$). This computational issue is addressed by first describing a new efficient and exact algorithm for kernel multiple change-point detection with an improved worst-case complexity that is quadratic in time and linear in space. It allows dealing with medium size signals (up to $n \approx 10^5$). Second, a faster but approximation algorithm is described. It is based on a low-rank approximation to the Gram matrix. It is linear in time and space. This approximation algorithm can be applied to large-scale signals ($n \geq 10^6$). These exact and approximation algorithms have been implemented in \texttt{R} and \texttt{C} for various kernels. The computational and statistical performances of these new algorithms have been assessed through empirical experiments. The runtime of the new algorithms is observed to be faster than that of other considered procedures. Finally, simulations confirmed the higher statistical accuracy of kernel-based approaches to detect changes that are not only in the mean. These simulations also illustrate the flexibility of kernel-based approaches to analyze complex biological profiles made of DNA copy number and allele B frequencies. An R package implementing the approach will be made available on github

Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it - an improved and generalized version of Bayesian Blocks (Scargle 1998) - that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multi-variate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by (Arias-Castro, Donoho and Huo 2003). In the spirit of Reproducible Research (Donoho et al. 2008) all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.Comment: Added some missing script files and updated other ancillary data (code and data files). To be submitted to the Astophysical Journa

Bayesian Detection of Changepoints in Finite-State Markov Chains for Multiple Sequences

We consider the analysis of sets of categorical sequences consisting of piecewise homogeneous Markov segments. The sequences are assumed to be governed by a common underlying process with segments occurring in the same order for each sequence. Segments are defined by a set of unobserved changepoints where the positions and number of changepoints can vary from sequence to sequence. We propose a Bayesian framework for analyzing such data, placing priors on the locations of the changepoints and on the transition matrices and using Markov chain Monte Carlo (MCMC) techniques to obtain posterior samples given the data. Experimental results using simulated data illustrates how the methodology can be used for inference of posterior distributions for parameters and changepoints, as well as the ability to handle considerable variability in the locations of the changepoints across different sequences. We also investigate the application of the approach to sequential data from two applications involving monsoonal rainfall patterns and branching patterns in trees

Joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a Bayesian sampling approach

International audienceWe propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared to parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However, an extension to models with unknown model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals