| Extremal Families and Systems of Sufficient Statistics 1988 Edition Contributor(s): Lauritzen, Steffen L. (Author) |
|
 |
ISBN: 0387968725 ISBN-13: 9780387968728 Publisher: Springer OUR PRICE: $132.05 Product Type: Paperback - Other Formats Published: November 1988 Annotation: This book surveys results in the area sometimes denoted as "partial exchangeability" of "de Finetti type theorems." It is to be seen as an attempt to give sense to the general idea that there is a strong coupling between a statistical model and the statistical analysis. So strong that there is a canonical mathematical construction leading from the analysis to the model. Special sections are devoted to the study of sufficiency, of triviality of tails of Markov chains, studied e.g. by coupling methods, Martin boundaries and projective limits of Markov kernels and Polish spaces. In addition, many examples of extreme point models are treated in detail. This book is intended for researchers and graduate students in mathematical statistics and probability. |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Science | History - Mathematics | Applied |
| Dewey: 519.5 |
| LCCN: 88212318 |
| Series: Texts and Monographs in Computer Science |
| Physical Information: 0.6" H x 6.14" W x 9.21" (0.90 lbs) 268 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The pOint of view behind the present work is that the connection between a statistical model and a statistical analysis-is a dua- lity (in a vague sense). In usual textbooks on mathematical statistics it is often so that the statistical model is given in advance and then various in- ference principles are applied to deduce the statistical ana- lysis to be performed. It is however possible to reverse the above procedure: given that one wants to perform a certain statistical analysis, how can this be expressed in terms of a statistical model? In that sense we think of the statistical analysis and the stati- stical model as two ways of expressing the same phenomenon, rather than thinking of the model as representing an idealisation of "truth" and the statistical analysis as a method of revealing that truth to the scientist. It is not the aim of the present work to solve the problem of giving the correct-anq final mathematical description of the quite complicated relation between model and analysis. We have rather restricted ourselves to describe a particular aspect of this, formulate it in mathematical terms, and then tried to make a rigorous and consequent investigation of that mathematical struc- ture. |
