Our motivation for writing this book was a dissatisfaction with the many books with titles hke Foundations of Statistics. These books provide a needed description of the subject with examples of various statistical methods; but they do not satisfy the discerning reader because they do not explain why certain conclusions may be drawn from certain data and they do not discuss how statistics, the subject, meshes with the scientific process. We naively set out to fill in these gaps, but the situation is not so simple. What is desired is a tool the one true statistics which can be applied to data...

This monograph is the first book-length exposition of ranked set sampling. But, the subject matter is by no means new. The original notion of ranked set sampling, though not the technical term, was proposed by McIntyre in 1952. It was buried in the literature for quite a while. Its value was only re-discovered in recent years because of its cost-effective nature. Now, ranked set sampling has attracted practical interest in application areas such as agriculture, forestry, ecological and environmental science, and medical studies etc .. The theoretical foundations of the method has also been...

Time series and random ?elds are main topics in modern statistical techniques. They are essential for applications where randomness plays an important role. Indeed, physical constraints mean that serious modelling cannot be done - ing only independent sequences. This is a real problem because asymptotic properties are not always known in this case. Thepresentworkisdevotedtoprovidingaframeworkforthecommonlyused time series. In order to validate the main statistics, one needs rigorous limit theorems. In the ?eld of probability theory, asymptotic behavior of sums may or may not be analogous to...

In the present book, we have put together the basic theory of the units and cuspidal divisor class group in the modular function fields, developed over the past few years. Let i) be the upper half plane, and N a positive integer. Let r(N) be the subgroup of SL (Z) consisting of those matrices == 1 mod N. Then r(N)i) 2 is complex analytic isomorphic to an affine curve YeN), whose compactifi cation is called the modular curve X(N). The affine ring of regular functions on yeN) over C is the integral closure of C j] in the function field of X(N) over C. Here j is the classical modular function....

This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic...

The present monograph is a comprehensive summary of the research on visibility in random fields, which I have conducted with the late Professor Micha Yadin for over ten years. This research, which resulted in several published papers and technical reports (see bibliography), was motivated by some military problems, which were brought to our attention by Mr. Pete Shugart of the US Army TRADOC Systems Analysis Activity, presently called US Army TRADOC Analysis Command. The Director ofTRASANA at the time, the late Dr. Wilbur Payne, identified the problems and encouraged the support and funding...

The book deals with bilinear forms in real random vectors and their generalizations as well as zonal polynomials and their applications in handling generalized quadratic and bilinear forms. The book is mostly self-contained. It starts from basic principles and brings the readers to the current research level in these areas. It is developed with detailed proofs and illustrative examples for easy readability and self-study. Several exercises are proposed at the end of the chapters. The complicated topic of zonal polynomials is explained in detail in this book. The book concentrates on the...

The articles in this volume present the state of the art in a variety of areas of discrete probability, including random walks on finite and infinite graphs, random trees, renewal sequences, Stein's method for normal approximation and Kohonen-type self-organizing maps. This volume also focuses on discrete probability and its connections with the theory of algorithms. Classical topics in discrete mathematics are represented as are expositions that condense and make readable some recent work on Markov chains, potential theory and the second moment method. This volume is suitable for...

Demonstrates how Bayesian methods allow complex neural network models to be used without the overfitting that can occur with traditional training methods. The text presents an insight into complex Baynesian models by a theoretical investigation of priors over functions that underlie them.