High-Dimensional Probability


Book Description

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.




Dyadic Decision Making


Book Description

Recent research on joint or dyadic decision making has received renewed attention from behavioral scientists. This interest is due mostly to the advances in analytic and conceptual models used to study interaction processes. A number of related disciplines have used distinctive paradigms to study the same focal problem: namely, the processes by which two people interact, come to resolve a problem and, finally, reach a decision. Dyadic Decision Making presents in a single, integrated volume the conceptual and analytic strategies developed in communications research, marketing, psychology and sociology to investigate joint decision making.




Dyadic Data Analysis


Book Description

Interpersonal phenomena such as attachment, conflict, person perception, learning, and influence have traditionally been studied by examining individuals in isolation, which falls short of capturing their truly interpersonal nature. This book offers state-of-the-art solutions to this age-old problem by presenting methodological and data-analytic approaches useful in investigating processes that take place among dyads: couples, coworkers, parent and child, teacher and student, or doctor and patient, to name just a few. Rich examples from psychology and across the behavioral and social sciences help build the researcher's ability to conceptualize relationship processes; model and test for actor effects, partner effects, and relationship effects; and model and control for the statistical interdependence that can exist between partners. The companion website provides clarifications, elaborations, corrections, and data and files for each chapter.




The SAGE Handbook of Social Network Analysis


Book Description

This sparkling Handbook offers an unrivalled resource for those engaged in the cutting edge field of social network analysis. Systematically, it introduces readers to the key concepts, substantive topics, central methods and prime debates. Among the specific areas covered are: Network theory Interdisciplinary applications Online networks Corporate networks Lobbying networks Deviant networks Measuring devices Key Methodologies Software applications. The result is a peerless resource for teachers and students which offers a critical survey of the origins, basic issues and major debates. The Handbook provides a one-stop guide that will be used by readers for decades to come.




An Introduction to Probabilistic Number Theory


Book Description

Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.




Modeling Dyadic and Interdependent Data in the Developmental and Behavioral Sciences


Book Description

This book reviews methods of conceptualizing, measuring, and analyzing interdependent data in developmental and behavioral sciences. Quantitative and developmental experts describe best practices for modeling interdependent data that stem from interactions within families, relationships, and peer groups, for example. Complex models for analyzing longitudinal data, such as growth curves and time series, are also presented. Many contributors are innovators of the techniques and all are able to clearly explain the methodologies and their practical problems including issues of measurement, missing data, power and sample size, and the specific limitations of each method. Featuring a balance between analytic strategies and applications, the book addresses: The Actor-Partner Interdependence Model for analyzing influence between two individuals The Intraclass Correlational Approach for analyzing distinguishable roles (parent-child) or exchangeable (same-sex) dyadic data The Social Relations Model for analyzing group interdependency Social Network Analysis approaches for relationships between individuals This book is intended for graduate students and researchers across the developmental, social, behavioral, and educational sciences. It is an excellent research guide and a valuable resource for advanced methods courses.




Analysis in Banach Spaces


Book Description

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.




Singular Integrals


Book Description