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Author: Masahito Hayashi Publisher: World Scientific ISBN: 981448198X Category : Science Languages : en Pages : 553
Book Description
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Author: Masahito Hayashi Publisher: World Scientific ISBN: 981448198X Category : Science Languages : en Pages : 553
Book Description
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Author: O. E. Barndorff-Nielsen Publisher: Springer ISBN: 9781489932112 Category : Mathematics Languages : en Pages : 360
Book Description
Our book Asymptotic Techniquesfor Use in Statistics was originally planned as an account of asymptotic statistical theory, but by the time we had completed the mathematical preliminaries it seemed best to publish these separately. The present book, although largely self-contained, takes up the original theme and gives a systematic account of some recent developments in asymptotic parametric inference from a likelihood-based perspective. Chapters 1-4 are relatively elementary and provide first a review of key concepts such as likelihood, sufficiency, conditionality, ancillarity, exponential families and transformation models. Then first-order asymptotic theory is set out, followed by a discussion of the need for higher-order theory. This is then developed in some generality in Chapters 5-8. A final chapter deals briefly with some more specialized issues. The discussion emphasizes concepts and techniques rather than precise mathematical verifications with full attention to regularity conditions and, especially in the less technical chapters, draws quite heavily on illustrative examples. Each chapter ends with outline further results and exercises and with bibliographic notes. Many parts of the field discussed in this book are undergoing rapid further development, and in those parts the book therefore in some respects has more the flavour of a progress report than an exposition of a largely completed theory.
Author: Samriddha Lahiry Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Recent breakthroughs in quantum technology, suchas quantum computing, communication, and metrology have given rise to questions related to quantum measurements which can be formulated in the language of mathematical statistics. Since quantum mechanics is fundamentally non-commutative in nature, statistical inference for these problems also involves dealing with such non-commutative structures. Moreover, inference in quantum statistics based on the laws of quantum probability deviates from inference in classical statistics, and the results often turn out to be different in a non-trivial way. In classical statistics a fundamental paradigm is approximating complicated experiments (families of laws, or models) by simpler ones. In particular, one establishes asymptotic equivalence between i.i.d. models indexed by a local parameter and a Gaussian shift model (with the shift given by the same local parameter). This approximation is called local asymptotic normality (LAN) and allows one to construct an estimator from a procedure in the Gaussian model with similar risk bounds. Local asymptotic equivalence can also been established between quantum i.i.d. models and quantum Gaussian models. In this thesis, we explore quantum statistical inference through the lens of local asymptotic equivalence and establish quantum counterparts of several results in classical statistics.
Author: Al?bert Nikolaevich Shiri?aev Publisher: World Scientific ISBN: 9789810241018 Category : Mathematics Languages : en Pages : 306
Book Description
This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is ?how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment?.
Author: Masahito Hayashi Publisher: Springer Science & Business Media ISBN: 3540302654 Category : Science Languages : en Pages : 430
Book Description
This graduate-level textbook provides a unified viewpoint of quantum information theory that merges key topics from both the information-theoretic and quantum- mechanical viewpoints. The text provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. This unified approach makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption.
Author: T. L. Lai Publisher: ISBN: Category : Mathematics Languages : en Pages : 560
Book Description
Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.
Author: Vladimir E. Bening Publisher: VSP ISBN: 9789067643238 Category : Mathematics Languages : en Pages : 312
Book Description
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Author: Masahito Hayashi
Author: Masahito Hayashi
Author: Dagmar Bruss (physicien).)
Author: O. E. Barndorff-Nielsen
Author: Samriddha Lahiry
Author: Al?bert Nikolaevich Shiri?aev
Author: Masahito Hayashi
Author: Ian Percival
Author: T. L. Lai
Author: Vladimir E. Bening
Author: B. L. S. Prakasa Rao