Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Inferring random change point from left-censored longitudinal data by segmented mechanistic nonlinear models, with application in HIV surveillance study

The primary goal of public health efforts to control HIV epidemics is to diagnose and treat people with HIV infection as soon as possible after seroconversion. The timing of initiation of antiretroviral therapy (ART) treatment after HIV diagnosis is, therefore, a critical population-level indicator that can be used to measure the effectiveness of public health programs and policies at local and national levels. However, population-based data on ART initiation are unavailable because ART initiation and prescription are typically measured indirectly by public health departments (e.g., with viral suppression as a proxy). In this paper, we present a random change-point model to infer the time of ART initiation utilizing routinely reported individual-level HIV viral load from an HIV surveillance system. To deal with the left-censoring and the nonlinear trajectory of viral load data, we formulate a flexible segmented nonlinear mixed effects model and propose a Stochastic version of EM (StEM) algorithm, coupled with a Gibbs sampler for the inference. We apply the method to a random subset of HIV surveillance data to infer the timing of ART initiation since diagnosis and to gain additional insights into the viral load dynamics. Simulation studies are also performed to evaluate the properties of the proposed method

Finding a Better Confidence Interval for a Single Regression Changepoint Using Different Bootstrap Confidence Interval Procedures

Recently a number of papers have been published in the area of regression changepoints but there is not much literature concerning confidence intervals for regression changepoints. The purpose of this paper is to find a better bootstrap confidence interval for a single regression changepoint. ( Better confidence interval means having a minimum length and coverage probability which is close to a chosen significance level). Several methods will be used to find bootstrap confidence intervals. Among those methods a better confidence interval will be presented

Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio

This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate parameter problems -- which include non-identifiable parameters and singular information matrices -- and change-point problems. The review focuses on the large-sample properties of the likelihood ratio statistic. We emphasize analytical solutions and acknowledge software implementations where available. We furthermore give summary insight about the possible tools to derivate the key results. Other approaches to hypothesis testing and connections to estimation are listed in the annotated bibliography of the Supplementary Material

Detecting abrupt changes in the spectra of high-energy astrophysical sources

Variable-intensity astronomical sources are the result of complex and often extreme physical processes. Abrupt changes in source intensity are typically accompanied by equally sudden spectral shifts, that is, sudden changes in the wavelength distribution of the emission. This article develops a method for modeling photon counts collected from observation of such sources. We embed change points into a marked Poisson process, where photon wavelengths are regarded as marks and both the Poisson intensity parameter and the distribution of the marks are allowed to change. To the best of our knowledge, this is the first effort to embed change points into a marked Poisson process. Between the change points, the spectrum is modeled nonparametrically using a mixture of a smooth radial basis expansion and a number of local deviations from the smooth term representing spectral emission lines. Because the model is over-parameterized, we employ an ℓ1ℓ1 penalty. The tuning parameter in the penalty and the number of change points are determined via the minimum description length principle. Our method is validated via a series of simulation studies and its practical utility is illustrated in the analysis of the ultra-fast rotating yellow giant star known as FK Com

Report of the study group on the further development of the precautionary approach to fishery management

Contributors: Asgeir Aglen, Tore Jakobsen, Dankert W. Skagen, Sigbjørn Meh

A Cross-Cohort Changepoint Model for Customer-Base Analysis

We introduce a new methodology that can capture and explain differences across a series of cohorts of new customers in a repeat-transaction setting. More specifically, this new framework, which we call a vector changepoint model, exploits the underlying regime structure in a sequence of acquired customer cohorts to make predictive statements about new cohorts for which the firm has little or no longitudinal transaction data. To accomplish this, we develop our model within a hierarchical Bayesian framework to uncover evidence of (latent) regime changes for each cohort-level parameter separately, while disentangling cross-cohort changes from calendar-time changes. Calibrating the model using multicohort donation data from a nonprofit organization, we find that holdout predictions for new cohorts using this model have greater accuracy—and greater diagnostic value—compared to a variety of strong benchmarks. Our modeling approach also highlights the perils of pooling data across cohorts without accounting for cross-cohort shifts, thus enabling managers to quantify their uncertainty about potential regime changes and avoid “old data” aggregation bias