Bayesian Sequential Change Point Detection And Hypotheses Testing Problems For Compound Poisson And Wiener Processes PDF Download
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Author | : Semih Onur Sezer |
Publisher | : |
Total Pages | : 234 |
Release | : 2006 |
Genre | : |
ISBN | : |
Download Bayesian Sequential Change-point Detection and Hypotheses Testing Problems for Compound Poisson and Wiener Processes Book in PDF, ePub and Kindle
Author | : Paul Jacob Plummer |
Publisher | : |
Total Pages | : 127 |
Release | : 2012 |
Genre | : Change-point problems |
ISBN | : |
Download Detecting Change-points in a Compound Poisson Process Book in PDF, ePub and Kindle
A statistical change point problem was first studied in the mid-1950s in the context of quality control in industrial processes. A change point is defined as a point in the time order when the probability distribution of a sequence of observations differs before and after that point. The literature of statistical change point has evolved over time and now includes a significant amount of scholarly work on change point analysis with many important applications in other disciplines such as economics, geosciences, medicine, and genetics, to name a few. This work examines the problem of locating changes in the distribution of a Compound Poisson Process where the variables being summed are iid normal and the number of variable follows Poisson. The maximum likelihood ratio for the location of the change point will be explored as well as an information criterion developed, for the case of known variance, while a Bayesian approach is used to deal with the case including change in variance. These results can be applied in any field of study where an interest in locating changes not only in the parameter of a normally distributed data set but also in the rate of their occurrence. It has direct application to the study of gene expression data in cancer research, where it is known that the distances between the genes can affect their expression level.
Author | : S. Zacks |
Publisher | : |
Total Pages | : 49 |
Release | : 1982 |
Genre | : Bayesian statistical decision theory |
ISBN | : |
Download Classical and Bayesian Approaches to the Change-point Problem Book in PDF, ePub and Kindle
The change-point problem can be considered one of the central problems of statistical inference, linking together statistical control theory, theory of estimation and testing hypotheses, classical and Bayesian approaches, fixed sample and sequential procedures. It is very often the case that observations are taken sequentially over time, or can be intrinsically ordered in some other fashion. The basic question is, therefore, whether the observations represent independent and identically distributed random variables, or whether at least one change in the distribution law has taken place. This is the fundamental problem in the statistical control theory, testing the stationarity of stochastic processes, estimation of the current position of a time-series, etc. Accordingly, a survey of all the major developments in statistical theory and methodology connected with the very general outlook of the change-point problem, would require review of the field of statistical quality control, the switching regression problems, inventory and queueing control, etc. The present review paper is therefore focused on methods developed during the last two decades for the estimation of the current position of the mean function of a sequence of random variables (or of a stochastic process); testing the null hypothesis of no change among given n observations, against the alternative of at most one change; the estimation of the location of the change-point(s) and some sequential detection procedures.
Author | : |
Publisher | : |
Total Pages | : 862 |
Release | : 2006 |
Genre | : Dissertations, Academic |
ISBN | : |
Download Dissertation Abstracts International Book in PDF, ePub and Kindle
Author | : David C. Mac Enany |
Publisher | : |
Total Pages | : 154 |
Release | : 1986 |
Genre | : |
ISBN | : |
Download Bayesian Sequential Hypothesis Testing Book in PDF, ePub and Kindle
Author | : Karlos J. Kachiashvili |
Publisher | : |
Total Pages | : 332 |
Release | : 2018-03 |
Genre | : Bayesian statistical decision theory |
ISBN | : 9781536131031 |
Download Constrained Bayesian Methods of Hypotheses Testing Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Research Report Book in PDF, ePub and Kindle
Author | : Goran Peskir |
Publisher | : |
Total Pages | : 18 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Solution of the Bayesian Sequential Testing Problem for a Poisson Process Book in PDF, ePub and Kindle
Author | : Karlos J. Kachiashvili |
Publisher | : |
Total Pages | : 363 |
Release | : 2018 |
Genre | : MATHEMATICS |
ISBN | : 9781536131048 |
Download Constrained Bayesian Methods of Hypotheses Testing Book in PDF, ePub and Kindle
"The problems of one of the basic branches of mathematical statistics – statistical hypotheses testing – are considered in this book. The intensive development of these methods began at the beginning of the last century. The basic results of modern theory of statistical hypotheses testing belong to the cohort of famous statisticians of this period: Fisher, Neyman-Pearson, Jeffreys and Wald (Fisher, 1925; Neyman and Pearson, 1928, 1933; Jeffreys, 1939; Wald, 1947a,b). Many other bright scientists have brought their invaluable contributions to the development of this theory and practice. As a result of their efforts, many brilliant methods for different suppositions about the character of random phenomena are under study, as well as their applications for solving very complicated and diverse modern problems. Since the mid-1970s, the author of this book has been engaged in the development of the methods of statistical hypotheses testing and their applications for solving practical problems from different spheres of human activity. As a result of this activity, a new approach to the solution of the considered problem has been developed, which was later named the Constrained Bayesian Methods (CBM) of statistical hypotheses testing. Decades were dedicated to the description, investigation and applications of these methods for solving different problems. The results obtained for the current century are collected in seven chapters and three appendices of this book. The short descriptions of existing basic methods of statistical hypotheses testing in relation to different CBM are examined in Chapter One. The formulations and solutions of conventional (unconstrained) and new (constrained) Bayesian problems of hypotheses testing are described in Chapter Two. The investigation of singularities of hypotheses acceptance regions in CBM and new opportunities in hypotheses testing are presented in Chapter Three. Chapter Four is devoted to the investigations for normal distribution. Sequential analysis approaches developed on the basis of CBM for different kinds of hypotheses are described in Chapter Five. The special software developed by the author for statistical hypotheses testing with CBM (along with other known methods) is described in Chapter Six. The detailed experimental investigation of the statistical hypotheses testing methods developed on the basis of CBM and the results of their comparison with other known methods are given in Chapter Seven. The formalizations of absolutely different problems of human activity such as hypotheses testing problems in the solution – of which the author was engaged in different periods of his life – and some additional information about CBM are given in the appendices. Finally, it should be noted that, for understanding the materials given in the book, the knowledge of the basics of the probability theory and mathematical statistics is necessary. I think that this book will be useful for undergraduate and postgraduate students in the field of mathematics, mathematical statistics, applied statistics and other subfields for studying the modern methods of statistics and their application in research. It will also be useful for researchers and practitioners in the areas of hypotheses testing, as well as the estimation theory who develop these new methods and apply them to the solutions of different problems. (Nova)"--
Author | : |
Publisher | : |
Total Pages | : 772 |
Release | : 1994 |
Genre | : Mathematical statistics |
ISBN | : |
Download Current Index to Statistics, Applications, Methods and Theory Book in PDF, ePub and Kindle
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.