scholarly journals Bayesian Online Learning of the Hazard Rate in Change-Point Problems

2010 ◽  
Vol 22 (9) ◽  
pp. 2452-2476 ◽  
Author(s):  
Robert C. Wilson ◽  
Matthew R. Nassar ◽  
Joshua I. Gold
Keyword(s):  
Change Point ◽  
Stock Price ◽  
Hazard Rate ◽  
Real Data ◽  
Generative Models ◽  
Ideal Observer ◽  
Change Points ◽  
Brain State ◽  
Observer Model ◽  
Change Point Models

Change-point models are generative models of time-varying data in which the underlying generative parameters undergo discontinuous changes at different points in time known as change points. Change-points often represent important events in the underlying processes, like a change in brain state reflected in EEG data or a change in the value of a company reflected in its stock price. However, change-points can be difficult to identify in noisy data streams. Previous attempts to identify change-points online using Bayesian inference relied on specifying in advance the rate at which they occur, called the hazard rate (h). This approach leads to predictions that can depend strongly on the choice of h and is unable to deal optimally with systems in which h is not constant in time. In this letter, we overcome these limitations by developing a hierarchical extension to earlier models. This approach allows h itself to be inferred from the data, which in turn helps to identify when change-points occur. We show that our approach can effectively identify change-points in both toy and real data sets with complex hazard rates and how it can be used as an ideal-observer model for human and animal behavior when faced with rapidly changing inputs.

Change-Point Models

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Survival Time ◽  
Change Point ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Real Data ◽  
Survival Times ◽  
Time Data ◽  
Probability Models ◽  
Kaplan Meier ◽  
Change Point Models

This chapter investigates change-point (hazard rate) probability models for the random survival time in some population of interest. A parametric probability distribution is assumed with parameters to be estimated from a sample of observed survival times. If a change-point parameter, denoted by τ‎, is included to represent the time at which there is a discrete change in hazard rate, then the model is non-standard. The profile log-likelihood, with τ‎ as profiling parameter, has a discontinuous jump at every τ‎ equal to a sampled value, becoming unbounded as τ‎ tends to the largest observation. It is known that maximum likelihood estimation can still be used provided the range of τ‎ is restricted. It is shown that the alternative maximum product of spacings method is consistent without restriction on τ‎. Censored observations which commonly occur in survival-time data can be accounted for using Kaplan-Meier estimation. A real data numerical example is given.

scholarly journals Closed-Form Estimation of Multiple Change-Point Models

2013 ◽  
Author(s):  
Greg Jensen
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Change Point ◽  
Marginal Likelihood ◽  
Stationary Time Series ◽  
Change Points ◽  
Model Complexity ◽  
Marginal Model ◽  
General Strategy ◽  
Change Point Models

Identifying discontinuities (or change-points) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood, a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described.

Modeling Two-Dimensional Framework for Multi-Upgradations of a Software with Change Point

2016 ◽  
Vol 23 (06) ◽  
pp. 1640008 ◽  
Author(s):  
Anshul Tickoo ◽  
Ajit K. Verma ◽  
Sunil K. Khatri ◽  
P. K. Kapur
Keyword(s):  
Fault Detection ◽  
Change Point ◽  
Detection Rate ◽  
Real Data ◽  
Testing Time ◽  
Two Dimensional ◽  
Data Set ◽  
Software Companies ◽  
Business Efficiency ◽  
Change Point Models

Across the globe almost every organization is dependent on information technology for increasing their business efficiency. This has led to huge demand for reliable and good quality software. Innovation is most important to attain success in software industry. Software companies need to keep bringing upgradations or add-ons in the software to compete in the market. In the present framework we propose a generalized mathematical modeling for multiple software releases. In this framework we examine the collective effect of testing time and resources using Cobb–Douglas production function for defining the failure phenomenon using a software reliability growth model (SRGM). In this paper, we consider the practical scenario where there is a possibility of change in the fault detection rate. Fault detection rate can be affected by various factors like testing environment, testing strategy and allocation of resources. Change in these factors during testing phase can lead to increase or decrease in failure intensity function. The time point at which abrupt fluctuations in fault detection rate take place is known as change point. In this paper, a generalized framework for developing a two-dimensional SRGM with change point for multiple software releases has been discussed. We have derived various existing change point models using the proposed framework. The developed models have been validated on real data set.

scholarly journals The Consistency of the CUSUM-Type Estimator of the Change-Point and Its Application

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2113
Author(s):  
Saisai Ding ◽  
Xiaoqin Li ◽  
Xiang Dong ◽  
Wenzhi Yang
Keyword(s):  
Stock Returns ◽  
Change Point ◽  
Convergence Rates ◽  
Real Data ◽  
Change Point Analysis ◽  
Point Analysis ◽  
Special Cases ◽  
The Family ◽  
Potential Applications ◽  
Change Point Models

In this paper, we investigate the CUSUM-type estimator of mean change-point models based on m-asymptotically almost negatively associated (m-AANA) sequences. The family of m-AANA sequences contains AANA, NA, m-NA, and independent sequences as special cases. Under some weak conditions, some convergence rates are obtained such as OP(n1/p−1), OP(n1/p−1log1/pn) and OP(nα−1), where 0≤α<1 and 1<p≤2. Our rates are better than the ones obtained by Kokoszka and Leipus (Stat. Probab. Lett., 1998, 40, 385–393). In order to illustrate our results, we do perform simulations based on m-AANA sequences. As important applications, we use the CUSUM-type estimator to do the change-point analysis based on three real data such as Quebec temperature, Nile flow, and stock returns for Tesla. Some potential applications to change-point models in finance and economics are also discussed in this paper.

scholarly journals Closed-Form Estimation of Multiple Change-Point Models

2013 ◽  
Author(s):  
Greg Jensen
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Change Point ◽  
Marginal Likelihood ◽  
Stationary Time Series ◽  
Change Points ◽  
Model Complexity ◽  
Marginal Model ◽  
General Strategy ◽  
Change Point Models

Identifying discontinuities (or change-points) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood, a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described.

scholarly journals Closed-Form Estimation of Multiple Change-Point Models

2013 ◽  
Author(s):  
Greg Jensen
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Change Point ◽  
Marginal Likelihood ◽  
Stationary Time Series ◽  
Change Points ◽  
Model Complexity ◽  
Marginal Model ◽  
General Strategy ◽  
Change Point Models

Identifying discontinuities (or change-points) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood, a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described.

scholarly journals Timing of onset and rate of decline in learning and retention in the pre-dementia phase of Alzheimer’s disease

2019 ◽  
Vol 25 (7) ◽  
pp. 699-705 ◽  
Author(s):  
Ellen Grober ◽  
Yang An ◽  
Richard B. Lipton ◽  
Claudia Kawas ◽  
Susan M. Resnick
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Free Recall ◽  
Change Point ◽  
Change Points ◽  
Immediate Recall ◽  
Initial Learning ◽  
Rate Of Decline ◽  
Change Point Models ◽  
Selective Reminding Test

AbstractObjective: To examine trajectories of declines in learning and retention during the predementia phase of Alzheimer’s disease (AD) using the picture version of the Free and Cued Selective Reminding Test with Immediate Recall (pFCSRT+IR). Method: Learning was defined by the sum of free recall over three test trials. Retention was defined in two ways: by delayed free recall (DFR) and by savings; DFR adjusted for learning. The performances of 217 incident AD cases from the Baltimore Longitudinal Study of Aging (BLSA) were aligned based on the time that AD was first diagnosed. The predementia phase of learning and retention decline was assessed using change point models in which cognitive trajectories are described by a series of linear components with knots delineating times of accelerating decline. Results: Trajectories for both learning and DFR had two change points: the first at 6.58 (95% confidence intervals (CI): 6.56, 6.60) to 7.29 (95% CI: 6.13, 8.46) years before diagnosis followed by gradual decline over the next 4 years, and a second acceleration of decline 1.89 (0.56, 3.24) to 2.93 (95% CI: 1.56, 4.30) years before diagnosis. The change points for DFR were not significantly earlier in the predementia phase than the change points for learning. Savings had one change point, 5.3 (95% CI: 3.56, 7.04) years before diagnosis. Conclusion: Both learning and DFR showed similar profiles of decline in the years prior to the clinical diagnosis of AD. When delayed recall was adjusted for initial learning, the measure was less sensitive to early disease. (JINS, 2019, 25, 699–705)

BAYESIAN IDENTIFICATION OF MULTIPLE CHANGE POINTS IN POISSON DATA

2005 ◽  
Vol 08 (04) ◽  
pp. 465-482 ◽  
Author(s):  
R. H. LOSCHI ◽  
F. R. B. CRUZ
Keyword(s):  
Change Point ◽  
Medical Diagnosis ◽  
Real Data ◽  
Identification Problem ◽  
Change Points ◽  
Data Sequence ◽  
Industrial Control ◽  
Bayesian Identification ◽  
Subject Areas ◽  
Poisson Data

The identification of multiple change points is a problem shared by many subject areas, including disease and criminality mapping, medical diagnosis, industrial control, and finance. An algorithm based on the Product Partition Model (PPM) is developed to solve the multiple change point identification problem in Poisson data sequences. In order to address the PPM, a simple and easy way to implement Gibbs sampling scheme is derived. A sensitivity analysis is performed, for different prior specifications. The algorithm is then applied to the analysis of a real data sequence. The results show that the method is quite effective and provides useful inferences.

scholarly journals Closed-Form Estimation of Multiple Change-Point Models

2013 ◽  
Author(s):  
Greg Jensen
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Change Point ◽  
Marginal Likelihood ◽  
Stationary Time Series ◽  
Change Points ◽  
Model Complexity ◽  
Marginal Model ◽  
General Strategy ◽  
Change Point Models

Identifying discontinuities (or change-points) in otherwise stationary time series is a powerful analytic tool. This paper outlines a general strategy for identifying an unknown number of change-points using elementary principles of Bayesian statistics. Using a strategy of binary partitioning by marginal likelihood, a time series is recursively subdivided on the basis of whether adding divisions (and thus increasing model complexity) yields a justified improvement in the marginal model likelihood. When this approach is combined with the use of conjugate priors, it yields the Conjugate Partitioned Recursion (CPR) algorithm, which identifies change-points without computationally intensive numerical integration. Using the CPR algorithm, methods are described for specifying change-point models drawn from a host of familiar distributions, both discrete (binomial, geometric, Poisson) and continuous (exponential, Gaussian, uniform, and multiple linear regression), as well as multivariate distribution (multinomial, multivariate normal, and multivariate linear regression). Methods by which the CPR algorithm could be extended or modified are discussed, and several detailed applications to data published in psychology and biomedical engineering are described.

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