Set At Random
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| Author | : Ilya Molchanov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 508 |
| Release | : 2005-05-11 |
| Genre | : Mathematics |
| ISBN | : 9781852338923 |
This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
| Author | : John Goutsias |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 417 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461219426 |
This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "Application and Theory of Random Sets." We would like to thank the scientific organizers: John Goutsias (Johns Hopkins University), Ronald P.S. Mahler (Lockheed Martin), and Hung T. Nguyen (New Mexico State University) for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the Army Research Office (ARO), the Office ofNaval Research (0NR), and the Eagan, MinnesotaEngineering Center ofLockheed Martin Tactical Defense Systems, whose financial support made the summer program possible. Avner Friedman Robert Gulliver v PREFACE "Later generations will regard set theory as a disease from which one has recovered. " - Henri Poincare Random set theory was independently conceived by D.G. Kendall and G. Matheron in connection with stochastic geometry. It was however G.
| Author | : Ilya Molchanov |
| Publisher | : Cambridge University Press |
| Total Pages | : 199 |
| Release | : 2018-04-12 |
| Genre | : Business & Economics |
| ISBN | : 1107121205 |
This is the first full-length study of how the theory of random sets can be applied in econometrics.
| Author | : Branko Ristic |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 184 |
| Release | : 2013-04-15 |
| Genre | : Technology & Engineering |
| ISBN | : 1461463165 |
This book discusses state estimation of stochastic dynamic systems from noisy measurements, specifically sequential Bayesian estimation and nonlinear or stochastic filtering. The class of solutions presented in this book is based on the Monte Carlo statistical method. Although the resulting algorithms, known as particle filters, have been around for more than a decade, the recent theoretical developments of sequential Bayesian estimation in the framework of random set theory have provided new opportunities which are not widely known and are covered in this book. This book is ideal for graduate students, researchers, scientists and engineers interested in Bayesian estimation.
| Author | : Hung T. Nguyen |
| Publisher | : CRC Press |
| Total Pages | : 268 |
| Release | : 2006-03-27 |
| Genre | : Mathematics |
| ISBN | : 1420010611 |
The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that i
| Author | : Shoumei Li |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 414 |
| Release | : 2002-10-31 |
| Genre | : Mathematics |
| ISBN | : 9781402009181 |
This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as Hölmander's embedding theorem, notions of various convergence of sets and fuzzy sets, Aumann integrals, conditional expectations, selection theorems, measurability and integrability arguments for both set-valued and fuzzy set-valued random variables and newly obtained optimizations techniques based on invariant properties are also given.
| Author | : Shoumei Li |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 399 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 9401599327 |
After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.
| Author | : John Stephen Mullane |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 161 |
| Release | : 2011-05-19 |
| Genre | : Technology & Engineering |
| ISBN | : 3642213898 |
The monograph written by John Mullane, Ba-Ngu Vo, Martin Adams and Ba-Tuong Vo is devoted to the field of autonomous robot systems, which have been receiving a great deal of attention by the research community in the latest few years. The contents are focused on the problem of representing the environment and its uncertainty in terms of feature based maps. Random Finite Sets are adopted as the fundamental tool to represent a map, and a general framework is proposed for feature management, data association and state estimation. The approaches are tested in a number of experiments on both ground based and marine based facilities.
| Author | : James E. Gentle |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2013-03-14 |
| Genre | : Computers |
| ISBN | : 147572960X |
Monte Carlo simulation has become one of the most important tools in all fields of science. This book surveys the basic techniques and principles of the subject, as well as general techniques useful in more complicated models and in novel settings. The emphasis throughout is on practical methods that work well in current computing environments.
| Author | : R. J. Adler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 455 |
| Release | : 2009-01-29 |
| Genre | : Mathematics |
| ISBN | : 0387481168 |
This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
