# Workshop Programme

## for period 13 - 17 January 2014

### Inference for Change-Point and Related Processes

13 - 17 January 2014

Timetable

 Monday 13 January 10:00-11:30 Registration 11:30-12:30 Dahlhaus, R (Universität Heidelberg) Locally Stationary Processes - An Overview Sem 1 The talk gives an overview on locally stationary processes. After summarizing the basic models and techniques we discuss in more detail the likelihood theory for locally stationary processes and empirical process theory for the theoretical treatment of statistical inference. We also present a Taylor type expansion for locally stationary processes in terms of so called derivative processes and show how these techniques can be used for investigating the statistical properties of estimators. 12:30-13:30 Lunch at Wolfson Court 14:00-15:00 Siegmund, D (Stanford University) Change-point detection and analysis Sem 1 Change-point detection had its origins almost sixty years ago in the work of Page, Shiryayev, and Lorden, who focused on sequential detection of a change-point in an observed process. The observations were typically regarded as measurements of the quality of a continuous production process, and the change-point indicated a deterioration in quality that must be detected and corrected. Recent applications, especially in genetics and in fMRI analysis, have led to a variety of new fixed sample change-point problems and other problems of local signal detection having the same essential structure. In this talk I will review this history and common features of likelihood based approaches. 15:00-15:30 Afternoon Tea 15:30-16:30 Nason, G (University of Bristol) Detection and Exploitation of Nonstationarities in Time Series Data Sem 1 In recent years, with disciplines becoming increasingly quantitative, time series exhibiting nonstationary characteristics have proliferated. Such proliferation is partly due to our improved ability to collect longer series enabling the detection of nonstationarities and nonlinearities that could not be found before. Time series are more complex too, not only are we faced by classical univariate and multivariate series but time series on graphs, manifolds and fractal-like domains. This talk provides an overview on the detection of nonstationarities and how to exploit them to provide a richer understanding of their underlying characteristics. We exhibit these techniques on a variety of data sets arising in earth sciences, economics and epidemics. 16:30-18:00 Welcome Wine Reception and Poster Session
 Wednesday 15 January 09:30-10:00 Nunes, M (Lancaster University) Analysis of time series observed on networks Sem 1 In this talk we consider analysis problems for time series that are observed at nodes of a large network structure. Such problems commonly appear in a vast array of fields, such as environmental time series observed at different spatial locations or measurements from computer system monitoring. The time series observed on the network might exhibit different characteristics such as nonstationary behaviour or strong correlation, and the nodal series evolve according to the inherent spatial structure. The new methodology we develop hinges on reducing dimensionality of the original data through a change of basis. The basis we propose is a second generation wavelet basis which operates on spatial structures. As such, the (large) observed data is replaced by data over a reduced network topology. We give examples of the potential of this dimension reduction method for time series analysis tasks. This is joint work with Marina Knight (University of York) and Guy Nason (University of Bristol). 10:00-10:30 Fuh, C-D (National Central University, Taiwan) Decentralized Quickest Change Detection in Hidden Markov Models for Sensor Networks Sem 1 The decentralized quickest change detection problem is studied in sensor networks, where a set of sensors take observations from a hidden Markov model (HMM) and send sensor messages to a fusion center, which makes a final decision when observations are stopped. It is assumed that the parameter $\theta$ in the HMM model changes from $\theta_0$ to $\theta_1$ at some unknown time. The problem is to determine the policies at the sensor and fusion center levels to jointly optimize the detection delay subject to the average run length (ARL) to false alarm constraint. The primary goal of this paper is to investigate how to choose the best binary stationary quantizers from the both theoretical and computational viewpoints when a CUSUM-type scheme is used at the fusion center. Further research is also given. 10:30-11:00 Harchaoui, Z (INRIA and LJK) Nonparametric change-point detection with sparse alternatives Sem 1 We consider the problem of detecting the change in mean in a sequence of Gaussian vectors. We assume that the change happens only in some of the components of the vector. We construct a nonparametric testing procedure that is adaptive to the number of changing components. Under high-dimensional assumptions we obtain the detection boundary and show the rate optimality of the test. 11:00-11:30 Morning Coffee 11:30-12:15 Olhede, S (University College London) Modelling multivariate nonstationarity Sem 1 Co-authors: Adam Sykulski (UCL), Jonathan Lilly (NWRA), Jeffrey Early (NWRA) Nonstationarity, like all non-properties, is hard to pin down precisely, and to model sufficiently flexibly for realism, but at the same time model in a sufficiently constrained fashion to allow for good inference. Modelling is inevitably time or frequency domain, where the two branches of thinking are traditionally linked via the local spectrum, or another bilinear representation of the data. The resolution in the representation is constrained by the choice of representation. There are of course many alternatives to modelling the local Fourier transform, but these have been mainly parametric or have been developed for a specific application. A problem in general is chosing a representation that suits analysis of more than one series. We shall focus on how our notion of nonstationarity must change when thinking of such observations, focussing on what features are present in bivariate series, that cannot be found in univariate observations. 12:15-13:30 Lunch at Wolfson Court 13:30-14:00 Kirch, C (Karlsruhe Institute of Technology) Change-point tests based on estimating functions Sem 1 Many classical change-point tests are based on cumulative sums of estimating functions, where the most prominent example are quasi maximum likelihood scores. Examples include testing for changes in the location model, continuous linear and non-linear autoregressive time series as well as most recently changes in count time series. While classic theory deals with offline procedures where the full data set has been observed before a statistical decision about a change-point is made, the same principles can be used in sequential testing. The latter has gained some increased interest in the last decade, where initial parameter estimation is based on some historic data set with no change-point, before cumulative sum charts are used to monitor newly arriving data. In such a setup, asymptotics are carried out with the size of the historic data set increasing to infinity. In applications such a data set will typically exist as usually at least some data is collected before any reason able statistical inference can be made. In this talk we explain the underlying ideas and extract regularity conditions under which asymptotics both under the null hypothesis as well as alternative can be derived. We will illustrate the usefulness using different examples that have partly already been discussed in the literature. 14:00-14:30 Yau, C-Y (Chinese University of Hong Kong) Inference for multiple change-points in time series via likelihood ratio scan statistics Sem 1 We propose a Likelihood Ratio Scan Method (LRSM) for multiple change-points estimation in piecewise stationary processes. Using the idea of scan statistics, the computationally infeasible global multiple change-points estimation problem is reduced to a number of single change-point detection problems in various local windows. The computation can be performed efficiently with order $O(n\log n)$. Consistency for the estimated number and locations of the change-points are established. Moreover, a procedure for constructing confidence intervals for each of the change-point is developed. Simulation experiments show that LRSM outperforms other methods when the series length is large and the number of change-points is relatively small. 14:30-15:00 Eichler, M (Universiteit Maastricht) Non-stationary functional time series: an application to electricity supply and demand Sem 1 One main feature of electricity spot prices is the frequent occurrence of spikes, that is, of periods of extreme prices that are typically short-lived and during which the spot price exceeds its normal level many times over. Such spikes occur usually if the supply and demand curves that determine the spot price meet in their steeper parts. For a better assessment of the risk in such situation we propose to include the complete supply and demand curves to forecast spot prices. We model the spread between the supply and demand curve as a functional time series. The approach is based on a decomposition into eigenfunctions and model eigenvalues by a dynamic factor model. We find that the form of the spread does not remain stable over time but mostly evolves slowly over time. There are, however, few marked time points of sudden changes in the functional form of the spread. The project is ongoing work and the talk will cover some preliminary results. 15:00-15:30 Afternoon Tea 15:30-16:00 Pavlidis, N (Lancaster University) High-Dimensional Incremental Divisive Clustering under Population Drift Sem 1 Clustering is a central problem in data mining and statistical pattern recognition with a long and rich history. The advent of Big Data has introduced important challenges to existing clustering methods in the form of high-dimensional, high-frequency, time-varying streams of data. Up-to-date research on Big Data clustering has been almost exclusively focused on addressing individual aspects of the problem in isolation, largely ignoring whether and how the proposed methods can be extended to address the overall problem. We will discuss an incremental divisive clustering approach for high-dimensional data that has storage requirements that are low and more importantly independent of the stream size, and can identify changes in the population distribution that require a revision of the clustering result. 16:00-16:30 Heaton, T (Sheffield University) Shape smoothing (and what I hope to get from the Newton change-point program) Sem 1 This talk will present some ideas for smoothing manifolds that have been observed as discrete meshes subject to noise. We will discuss the potential to create wavelet-type bases informed by the geometry of the manifold. As opposed to global Laplace-Beltrami eigenfunctions, localised bases can be found through the lifting scheme. These bases should allow a parsimonious representation of the co-ordinate functions and allow denoising of the original shape via thresholding. I will also discuss some hopes that I have for the Newton Institute program and areas in change-point inference I am interested in working on. 16:30-17:00 Szajowski, K (Wroclaw University of Technology) Precision of Disorders Detection Sem 1 The lecture presents the results on the problem of change point detection for Markov processes generalizing the results contained in the publications [2], [4], [3] and [1]. The short description are as follows. A random sequence having segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each process are known and joint a priori distribution of the disorder moments is given. The detection of the disorder rarely is precise. The decision maker accepts some deviation in estimation of the disorder moment. In the models taken into account the aim is to indicate the change point with xed, bounded error with maximal probability. The case with various precision for over and under estimation of this point is analysed including situation when the disorder does not appears with positive probability is also included. The observed sequence, when the change point is known, has the Markov properties. The results explain the structure of optimal detector in various circumstances and shows new details of the solution construction as well insigni cantly extends range of application. The motivation for this investigation is the modelling of the attacks in the node of networks. The objectives is to detect one of the attack immediately or in very short time before or after it appearance with highest probability. The problem is reformulated to optimal stopping of the observed sequences. The detailed analysis of the problem is presented to show the form of optimal decision function. Key Words: disorder problem, sequential detection, optimal stopping, multi-variate optimization 19:30-22:00 Conference Dinner at Cambridge Union Society hosted by Cambridge Dining Company