Nowadays, Earth observation (EO) technology became an indispensable tool to help environmental monitoring, as well as their changes, for natural resources management, urban planning and development, water management and land use planning. In particular, radar EOs, unlike the optical ones, can be collected regardless of illumination and weather conditions. Multitemporal polarimetric synthetic aperture radar (PolSAR) images are useful source of information for detection and mapping the environmental changes, especially in wide areas, during the day and night and all weather conditions. Change detection methods can identify the change or no change conditions in land covers using the time series observations. In this paper a method is proposed for change detection in SAR remote sensing images. This method is based on the Change Point Analysis. The cumulative frequency of difference image, which contains the environmental changes, normally follows a specific class of statistical distribution. Gaussian mixture model is one of the most suitable models for Change Point Analysis. This model can efficiently estimate the parameters of mixture distribution. The intersection point of two distributions is a change point, which can be seen as a threshold. This threshold is then used to separate the change and no change classes. The proposed method is implemented and analyzed using three SAR data sets. The analytical evaluations of the final change maps from two of these data sets with reference data had the Kappa coefficients of 90% and 96% respectively. The other data set contained the multitemporal PolSAR images and had been acquired over an agricultural area. The changes in these images were enough reliable to be connected to the agricultural activities, such as crop growing stages and harvesting, based on an available crop map. Finally, the method was evaluated against the Otsu method, as one of the best threshold estimation methods, and the results showed the superiority of the proposed method, e.g.2% better in term of kappa coefficient.. As a result, the proposed method, can be efficiently employed for land cover change detection and monition in natural resources management.

The Kalman-Bucy filter is studied under different scenarios for observation and state equations, however, an important question is, how this filter may be applied to detect the change points. In this paper, using the Bayesian approach, a modified version of this filter is studied which has good and justifiable properties and is applied in change point analysis.

Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change, a linear trend and a known multiple number of changes in the Poisson rate. The Markov chain Monte Carlo is used to obtain posterior distributions of the change point parameters and corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the well-known c-, Poisson exponentially weighted moving average (EWMA) and Poisson cumulative sum (CUSUM) control charts for different change type scenarios. We also apply the Deviance Information Criterion as a model selection criterion in the Bayesian context, to find the best change point model for a given dataset where there is no prior knowledge about the change type in the process. In comparison with built-in estimators of EWMA and CUSUM charts and ML based estimators, the Bayesian estimator performs reasonably well and remains a strong alternative. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

We present a Bayesian analysis for recurrent events data using a nonhomogeneous mixed Poisson point process with a dynamic subject-specific frailty function and a dynamic baseline intensity function.The dynamic subject-specific frailty employs a dynamic piecewise constant function with a known pre-specified grid and the baseline intensity uses an unknown grid for the piecewise constant function. Implementation of Bayesian inference using a reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is developed to handle the change of the dimension in the parameter space for models with a random number of change points. A data set provided by Grubbs et al. (1991) with recurrent times to mammary tumors for 59 rats is used to illustrate the application of the new models. We compare several models including constant or piecewise constant subject-specific frailty and a fixed number or a random number for the change points in the baseline using the pseudo-marginal likelihood criterion. We show that models with a random number of change points in the baseline improve upon that of a fixed number.

In many practical cases, product or process quality is defined by frequency table of two or more qualitative variables. This frequency table is called contingency table. Monitoring the contingency tables is an area in statistical process control with many applications in industrial and service units. On the other hand, reducing quality costs is the most fundamental issue preoccupying the minds of managers. It is clear that a quicker diagnosis of the assignable causes can reduce the quality costs. Estimating change point by limiting the probable interval of change, reduces the cost and time of detecting assignable causes. In this research, using maximum likelihood approach, the step and linear drift change points estimators are proposed for multivariate multi-nominal contingency tables. After the change point, parameters are estimated with making the average in the proposed step estimator, and using the linear regression in the proposed linear drift estimator. Results of the simulations demonstrated that the proposed step change point estimator carries out very well in all shift types and shift magnitudes from small to large. Furthermore, the proposed estimator of the linear drift change point has relatively good performance in moderate changes. Finally, the proposed estimators’ performance is assessed by a numerical example.

In this paper, it is assumed that the mean of a normal process is monitored by a CUSUM control chart. When the control chart triggers a signal and declares that the process has gone out of control, a search process is started to find the time of change and the causes of going the process out of control. Several methods (plans) for finding the true (real) change point is proposed. It is shown that the plans which are based on the likelihood of the points in time perform better.