VLSI CADhas greatly bene?ted from the use of reduced ordered Binary Decision Diagrams (BDDs) and the clausal representation as a problem of Boolean Satis?ability (SAT), e.g. in logic synthesis, ver- cation or design-for-testability. In recent practical applications, BDDs are optimized with respect to new objective functions for design space exploration. The latest trends show a growing number of proposals to fuse the concepts of BDD and SAT. This book gives a modern presentation of the established as well as of recent concepts. Latest results in BDD optimization are given, c- ering di?erent aspects of paths in BDDs and the use of e?cient lower bounds during optimization. The presented algorithms include Branch ? and Bound and the generic A -algorithm as e?cient techniques to - plore large search spaces. ? The A -algorithm originates from Arti?cial Intelligence (AI), and the EDA community has been unaware of this concept for a long time. Re- ? cently, the A -algorithm has been introduced as a new paradigm to explore design spaces in VLSI CAD. Besides AI search techniques, the book also discusses the relation to another ?eld of activity bordered to VLSI CAD and BDD optimization: the clausal representation as a SAT problem.

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. Limit theorems for semimartingales form the basis of the martingale approximation approach. The methods of martingale approximation addressed in this book pertain to estimates of the rate of convergence in the central limit theorem and in the invariance principle. Some applications of martingale approximation are illustrated by the analysis of U-statistics, rank statistics, statistics of exchangeable variables and stochastic exponential statistics. Simplified results of stochastic analysis are given for use in investigations of many applied problems, including mathematical statistics, financial mathematics, mathematical biology, industrial mathematics and engineering.

This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.

The place in survival analysis now occupied by proportional hazards models and their generalizations is so large that it is no longer conceivable to offer a course on the subject without devoting at least half of the content to this topic alone. This book focuses on the theory and applications of a very broad class of models - proportional hazards and non-proportional hazards models, the former being viewed as a special case of the latter - which underlie modern survival analysis. Researchers and students alike will find that this text differs from most recent works in that it is mostly concerned with methodological issues rather than the analysis itself.

This volume is devoted to the most recent discoveries in mathematics and statistics. It also serves as a platform for knowledge and information exchange between experts from industrial and academic sectors. The book covers a wide range of topics, including mathematical analyses, probability, statistics, algebra, geometry, mathematical physics, wave propagation, stochastic processes, ordinary and partial differential equations, boundary value problems, linear operators, cybernetics and number and functional theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists.

Written to be more rigorous than other books on the same topics No other book on the topics explores programming and software in this manner Requires only undergraduate prerequisites

The book is devoted to the new trends in random evolutions and their various applications to stochastic evolutionary sytems (SES). Such new developments as the analogue of Dynkin's formulae, boundary value problems, stochastic stability and optimal control of random evolutions, stochastic evolutionary equations driven by martingale measures are considered. The book also contains such new trends in applied probability as stochastic models of financial and insurance mathematics in an incomplete market. In the famous classical financial mathematics Black-Scholes model of a (B, S) market for securities prices, which is used for the description of the evolution of bonds and stocks prices and also for their derivatives, such as options, futures, forward contracts, etc., it is supposed that the dynamic of bonds and stocks prices are set by a linear differential and linear stochastic differential equations, respectively, with interest rate, appreciation rate and volatility such that they are predictable processes. Also, in the Arrow-Debreu economy, the securities prices which support a Radner dynamic equilibrium are a combination of an Ito process and a random point process, with the all coefficients and jumps being predictable processes."

These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx) < 00, for some integer s;::: 3, and that Q is normalized, (1.2) J x(i)Q(dx) = 0 (1 ~ i ~ k), J x(i)x(j)Q(dx) = Dij (1 ~ i,j ~ k).

Multiparameter processes extend the existing one-parameter theory of random processes in an elegant way, and have found connections to diverse disciplines such as probability theory, real and functional analysis, group theory, analytic number theory, and group renormalization in mathematical physics, to name a few. This book lays the foundation of aspects of the rapidly developing subject of random fields, and is designed for a second graduate course in probability and beyond. Its intended audience is pure, as well as applied, mathematicians.

Apart from the underlying theme that all the contributions to this volume pertain to models set in an infinite dimensional space, they differ on many counts. Some were written in the early seventies while others are reports of ongoing research done especially with this volume in mind. Some are surveys of material that can, at least at this point in time, be deemed to have attained a satisfactory solution of the problem, while oth ers represent initial forays into an original and novel formulation. Some furnish alternative proofs of known, and by now, classical results, while others can be seen as groping towards and exploring formulations that have not yet reached a definitive form. The subject matter also has a wide leeway, ranging from solution concepts for economies to those for games and also including representation of preferences and discussion of purely mathematical problems, all within the rubric of choice variables belonging to an infinite dimensional space, interpreted as a commodity space or as a strategy space. Thus, this is a collective enterprise in a fairly wide sense of the term and one with the diversity of which we have interfered as little as possible. Our motivation for bringing all of this work under one set of covers was severalfold."

Statistics For Dummies, 2nd Edition (9781119293521) was previously published as Statistics For Dummies, 2nd Edition (9780470911082). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. The fun and easy way to get down to business with statistics Stymied by statistics? No fear? this friendly guide offers clear, practical explanations of statistical ideas, techniques, formulas, and calculations, with lots of examples that show you how these concepts apply to your everyday life. Statistics For Dummies shows you how to interpret and critique graphs and charts, determine the odds with probability, guesstimate with confidence using confidence intervals, set up and carry out a hypothesis test, compute statistical formulas, and more. * Tracks to a typical first semester statistics course * Updated examples resonate with today's students * Explanations mirror teaching methods and classroom protocol Packed with practical advice and real-world problems, Statistics For Dummies gives you everything you need to analyze and interpret data for improved classroom or on-the-job performance.

This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.

Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.

This book presents a unique collection of contributions from some of the foremost scholars in the field of risk and reliability analysis. Combining the most advanced analysis techniques with practical applications, it is one of the most comprehensive and up-to-date books available on risk-based engineering. All the fundamental concepts needed to conduct risk and reliability assessments are covered in detail, providing readers with a sound understanding of the field and making the book a powerful tool for students and researchers alike. This book was prepared in honor of Professor Armen Der Kiureghian, one of the fathers of modern risk and reliability analysis.

Proceedings of the 4th Pannonian Symposium on Mathematical Statistics, Bad Tatzmannsdorf, Austria, 4-10 September 1983, Volume A.

Statistic: A Concise Mathematical Introduction for Students and Scientists offers a one academic term text that prepares the student to broaden their skills in statistics, probability and inference, prior to selecting their follow-on courses in their chosen fields, whether it be engineering, computer science, programming, data sciences, business or economics. The book places focus early on continuous measurements, as well as discrete random variables. By invoking simple and intuitive models and geometric probability, discrete and continuous experiments and probabilities are discussed throughout the book in a natural way. Classical probability, random variables, and inference are discussed, as well as material on understanding data and topics of special interest. Topics discussed include: - Classical equally likely outcomes - Variety of models of discrete and continuous probability laws - Likelihood function and ratio - Inference - Bayesian statistics With the growth in the volume of data generated in many disciplines that is enabling the growth in data science, companies now demand statistically literate scientists and this textbook is the answer, suited for undergraduates studying science or engineering, be it computer science, economics, life sciences, environmental, business, amongst many others. Basic knowledge of bivariate calculus, R language, Matematica and JMP is useful, however there is an accompanying website including sample R and Mathematica code to help instructors and students.

This book surveys some of the important research work carried out by Indian scientists in the field of pure and applied probability, quantum probability, quantum scattering theory, group representation theory and general relativity. It reviews the axiomatic foundations of probability theory by A.N. Kolmogorov and how the Indian school of probabilists and statisticians used this theory effectively to study a host of applied probability and statistics problems like parameter estimation, convergence of a sequence of probability distributions, and martingale characterization of diffusions. It will be an important resource to students and researchers of Physics and Engineering, especially those working with Advanced Probability and Statistics.

With the critical role of statistics in the design, conduct, analysis and reporting of clinical trials or observational studies intended for regulatory purposes, numerous guidelines have been issued by regulatory authorities around the world focusing on statistical issues related to drug development. However, the available literature on this important topic is sporadic, and often not readily accessible to drug developers or regulatory personnel. This book provides a systematic exposition of the interplay between the two disciplines, including emerging themes pertaining to the acceleration of the development of pharmaceutical medicines to serve patients with unmet needs. Features: Regulatory and statistical interactions throughout the drug development continuum The critical role of the statistician in relation to the changing regulatory and healthcare landscapes Statistical issues that commonly arise in the course of drug development and regulatory interactions Trending topics in drug development, with emphasis on current regulatory thinking and the associated challenges and opportunities The book is designed to be accessible to readers with an intermediate knowledge of statistics, and can be a useful resource to statisticians, medical researchers, and regulatory personnel in drug development, as well as graduate students in the health sciences. The authors' decades of experience in the pharmaceutical industry and academia, and extensive regulatory experience, comes through in the many examples throughout the book.

Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields. New results have made it possible to obtain a detailed nonperturbative analysis of the multi-spin correlations. In particular, the book focuses on deformation analysis of the scaling functions of the Ising model, and will appeal to graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory.

In recent years statistical physics has made significant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as financial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become significant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.

This BASS book Series publishes selected high-quality papers reflecting recent advances in the design and biostatistical analysis of biopharmaceutical experiments - particularly biopharmaceutical clinical trials. The papers were selected from invited presentations at the Biopharmaceutical Applied Statistics Symposium (BASS), which was founded by the first Editor in 1994 and has since become the premier international conference in biopharmaceutical statistics. The primary aims of the BASS are: 1) to raise funding to support graduate students in biostatistics programs, and 2) to provide an opportunity for professionals engaged in pharmaceutical drug research and development to share insights into solving the problems they encounter. The BASS book series is initially divided into three volumes addressing: 1) Design of Clinical Trials; 2) Biostatistical Analysis of Clinical Trials; and 3) Pharmaceutical Applications. This book is the third of the 3-volume book series. The topics covered include: Targeted Learning of Optimal Individualized Treatment Rules under Cost Constraints, Uses of Mixture Normal Distribution in Genomics and Otherwise, Personalized Medicine - Design Considerations, Adaptive Biomarker Subpopulation and Tumor Type Selection in Phase III Oncology Trials, High Dimensional Data in Genomics; Synergy or Additivity - The Importance of Defining the Primary Endpoint, Full Bayesian Adaptive Dose Finding Using Toxicity Probability Interval (TPI), Alpha-recycling for the Analyses of Primary and Secondary Endpoints of Clinical Trials, Expanded Interpretations of Results of Carcinogenicity Studies of Pharmaceuticals, Randomized Clinical Trials for Orphan Drug Development, Mediation Modeling in Randomized Trials with Non-normal Outcome Variables, Statistical Considerations in Using Images in Clinical Trials, Interesting Applications over 30 Years of Consulting, Uncovering Fraud, Misconduct and Other Data Quality Issues in Clinical Trials, Development and Evaluation of High Dimensional Prognostic Models, and Design and Analysis of Biosimilar Studies.

This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution of common perpendicular arcs between, for instance, closed geodesics. Using tools from ergodic theory (including coding by topological Markov shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for them), the authors further prove the variational principle and rate of mixing for the geodesic flow on metric and simplicial trees-again without the need for any compactness or torsionfree assumptions. In a series of applications, using the Bruhat-Tits trees over non-Archimedean local fields, the authors subsequently prove further important results: the Mertens formula and the equidistribution of Farey fractions in function fields, the equidistribution of quadratic irrationals over function fields in their completions, and asymptotic counting results of the representations by quadratic norm forms. One of the book's main benefits is that the authors provide explicit error terms throughout. Given its scope, it will be of interest to graduate students and researchers in a wide range of fields, for instance ergodic theory, dynamical systems, geometric group theory, discrete subgroups of locally compact groups, and the arithmetic of function fields.