Change-point detection in environmental time series based on the informational approach

In this study, the Schwarz Information Criterion (SIC) is applied in order to detect change-points in the time series of surface water quality variables. The application of change-point analysis allowed detecting change-points in both the mean and the variance in series under study. Time variations in environmental data are complex and they can hinder the identification of the so-called change-points when traditional models are applied to this type of problems. The assumptions of normality and uncorrelation are not present in some time series, and so, a simulation study is carried out in order to evaluate the methodology’s performance when applied to non-normal data and/or with time correlation.

Change points detection in crime-related time series: an on-line fuzzy approach based on a shape space representation

The extension of traditional data mining methods to time series has been effectively applied to a wide range of domains such as finance, econometrics, biology, security, and medicine. Many existing mining methods deal with the task of change points detection, but very few provide a flexible approach. Querying specific change points with linguistic variables is particularly useful in crime analysis, where intuitive, understandable, and appropriate detection of changes can significantly improve the allocation of resources for timely and concise operations. In this paper, we propose an on-line method for detecting and querying change points in crime-related time series with the use of a meaningful representation and a fuzzy inference system. Change points detection is based on a shape space representation, and linguistic terms describing geometric properties of the change points are used to express queries, offering the advantage of intuitiveness and flexibility. An empirical evaluation is first conducted on a crime data set to confirm the validity of the proposed method and then on a financial data set to test its general applicability. A comparison to a similar change-point detection algorithm and a sensitivity analysis are also conducted. Results show that the method is able to accurately detect change points at very low computational costs. More broadly, the detection of specific change points within time series of virtually any domain is made more intuitive and more understandable, even for experts not related to data mining.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Feature Point Detection and Curve Approximation for Early Processing of Freehand Sketches

Freehand sketching is both a natural and crucial part of design, yet is unsupported by current design automation software. We are working to combine the flexibility and ease of use of paper and pencil with the processing power of a computer to produce a design environment that feels as natural as paper, yet is considerably smarter. One of the most basic steps in accomplishing this is converting the original digitized pen strokes in the sketch into the intended geometric objects using feature point detection and approximation. We demonstrate how multiple sources of information can be combined for feature detection in strokes and apply this technique using two approaches to signal processing, one using simple average based thresholding and a second using scale space.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the study of tephrochrology. In this paper, DFA is applied to compositional datasets of two different types of tephras from Mountain Ruapehu in New Zealand and Mountain Rainier in USA. The canonical variables from the analysis are further investigated with a statistical methodology of change-point problems in order to gain a better understanding of the change in compositional pattern over time. Finally, a special case of segmented regression has been proposed to model both the time of change and the change in pattern. This model can be used to estimate the age for the unknown tephras using Bayesian statistical calibration

Feature-point detection using distance transforms: Application to tracking tropical convective complexes

The identification, tracking, and statistical analysis of tropical convective complexes using satellite imagery is explored in the context of identifying feature points suitable for tracking. The feature points are determined based on the shape of complexes using the distance transform technique. This approach has been applied to the determination feature points for tropical convective complexes identified in a time series of global cloud imagery. The feature points are used to track the complexes, and from the tracks statistical diagnostic fields are computed. This approach allows the nature and distribution of organized deep convection in the Tropics to be explored.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

ϕ-Divergence Based Procedure for Parametric Change-Point Problems

This paper studies the change-point problem for a general parametric, univariate or multivariate family of distributions. An information theoretic procedure is developed which is based on general divergence measures for testing the hypothesis of the existence of a change. For comparing the exact sizes of the new test-statistic using the criterion proposed in Dale (J R Stat Soc B 48–59, 1986), a simulation study is performed for the special case of exponentially distributed random variables. A complete study of powers of the test-statistics and their corresponding relative local efficiencies, is also considered.

Studentized U-quantile processes under dependence with applications to change-point analysis

Peer reviewed

Asymptotic Change-Point Analysis of the Dependencies in Time Series

In recent papers, Wied and his coauthors have introduced change-point procedures to detect and estimate structural breaks in the correlation between time series. To prove the asymptotic distribution of the test statistic and stopping time as well as the change-point estimation rate, they use an extended functional Delta method and assume nearly constant expectations and variances of the time series. In this thesis, we allow asymptotically infinitely many structural breaks in the means and variances of the time series. For this setting, we present test statistics and stopping times which are used to determine whether or not the correlation between two time series is and stays constant, respectively. Additionally, we consider estimates for change-points in the correlations. The employed nonparametric statistics depend on the means and variances. These (nuisance) parameters are replaced by estimates in the course of this thesis. We avoid assuming a fixed form of these estimates but rather we use "blackbox" estimates, i.e. we derive results under assumptions that these estimates fulfill. These results are supplement with examples. This thesis is organized in seven sections. In Section 1, we motivate the issue and present the mathematical model. In Section 2, we consider a posteriori and sequential testing procedures, and investigate convergence rates for change-point estimation, always assuming that the means and the variances of the time series are known. In the following sections, the assumptions of known means and variances are relaxed. In Section 3, we present the assumptions for the mean and variance estimates that we will use for the mean in Section 4, for the variance in Section 5, and for both parameters in Section 6. Finally, in Section 7, a simulation study illustrates the finite sample behaviors of some testing procedures and estimates.

Méthode bayésienne de détection de rupture et/ou de tendance pour des données temporelles

Ce mémoire a pour but de déterminer des nouvelles méthodes de détection de rupture et/ou de tendance. Après une brève introduction théorique sur les splines, plusieurs méthodes de détection de rupture existant déjà dans la littérature seront présentées. Puis, de nouvelles méthodes de détection de rupture qui utilisent les splines et la statistique bayésienne seront présentées. De plus, afin de bien comprendre d’où provient la méthode utilisant la statistique bayésienne, une introduction sur la théorie bayésienne sera présentée. À l’aide de simulations, nous effectuerons une comparaison de la puissance de toutes ces méthodes. Toujours en utilisant des simulations, une analyse plus en profondeur de la nouvelle méthode la plus efficace sera effectuée. Ensuite, celle-ci sera appliquée sur des données réelles. Une brève conclusion fera une récapitulation de ce mémoire.

Méthode bayésienne de détection de rupture et/ou de tendance pour des données temporelles

Ce mémoire a pour but de déterminer des nouvelles méthodes de détection de rupture et/ou de tendance. Après une brève introduction théorique sur les splines, plusieurs méthodes de détection de rupture existant déjà dans la littérature seront présentées. Puis, de nouvelles méthodes de détection de rupture qui utilisent les splines et la statistique bayésienne seront présentées. De plus, afin de bien comprendre d’où provient la méthode utilisant la statistique bayésienne, une introduction sur la théorie bayésienne sera présentée. À l’aide de simulations, nous effectuerons une comparaison de la puissance de toutes ces méthodes. Toujours en utilisant des simulations, une analyse plus en profondeur de la nouvelle méthode la plus efficace sera effectuée. Ensuite, celle-ci sera appliquée sur des données réelles. Une brève conclusion fera une récapitulation de ce mémoire.

Structural Time Series Modeling: an Application to Environmental Variables

A structural time series model is one which is set up in terms of components which have a direct interpretation. In this paper, the discussion focuses on the dynamic modeling procedure based on the state space approach (associated to the Kalman filter), in the context of surface water quality monitoring, in order to analyze and evaluate the temporal evolution of the environmental variables, and thus identify trends or possible changes in water quality (change point detection). The approach is applied to environmental time series: time series of surface water quality variables in a river basin. The statistical modeling procedure is applied to monthly values of physico- chemical variables measured in a network of 8 water monitoring sites over a 15-year period (1999-2014) in the River Ave hydrological basin located in the Northwest region of Portugal.