Statistical Design and Analysis of Stability Studies
Illustrating how stability studies play an important role in drug safety and quality assurance, this book introduces the basic concepts of stability testing, focuses on short-term stability studies, and reviews several methods for estimating drug expiration dating periods. The author compares some commonly employed study designs and discusses both
Control System Analysis and Identification with Matlab(r)
This book covers block pulse and related functions for the analysis and identification of continuous and discrete-time systems. It covers 'functions related to block pulse functions' and pulse-width modulated generalized block pulse functions including their applications including MATLAB based examples.
Bayesian Regression Modeling with Inla
This book addresses the applications of extensively used regression models under a Bayesian framework. It emphasizes efficient Bayesian inference through integrated nested Laplace approximations (INLA) and real data analysis using R. The INLA method directly computes very accurate approximations to the posterior marginal distributions and is a p
Operational Procedures Describing Physical Systems
The authors examine topics in modern physics and offer a unitary and original treatment of the fundamental problems of the dynamics of physical systems, as well as a description of the nuclear matter within a framework of general relativity.
Stochastic H2/H ∞ Control: A Nash Game Approach
The H∞ control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H∞ control, and studies more complex and practically useful mixed H2/H∞ controller synthesis rather than the pure H∞ control. Different from the commonly used convex optimization method, this book applies
Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and Inla
The Integrated Nested Laplace Approximation is a popular method for approximate Bayesian inference. INLA is an alternative to other methods for Bayesian inference, such as Markov Chain Monte Carlo, that are more computationally demanding. In addition, the R-INLA package for the R statistical software provides a way to fit such models in practice
Practical Sampling Techniques
Second Edition offers a comprehensive presentation of scientific sampling principles and shows how to design a sample survey and analyze the resulting data. Demonstrates the validity of theorems and statements without resorting to detailed proofs.
Design and Analysis of Bridging Studies
Taking into account the International Conference Harmonisation E5 framework for bridging studies, this book covers the regulatory requirements, scientific and practical issues, and statistical methodology for designing and evaluating bridging studies and multiregional clinical trials. For bridging studies, the authors explore ethnic sensitivity,
Boundary Value Problems and Markov Processes
This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject. The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.
Bayesian Inference for Stochastic Processes
The book aims to introduce Bayesian inference methods for stochastic processes. The Bayesian approach has advantages compared to non-Bayesian, among which is the optimal use of prior information via data from previous similar experiments. Examples from biology, economics, and astronomy reinforce the basic concepts of the subject. R a
Sample Size Calculations for Clustered and Longitudinal Outcomes in Clinical Research
This book explains how to determine sample size for studies with correlated outcomes, which are widely implemented in medical, epidemiological, and behavioral studies. For clustered studies, the authors provide sample size formulas that account for variable cluster sizes and within-cluster correlation. For longitudinal studies, they present samp
Fractional Order Processes
The book focusses on applications of triangular orthogonal function in fractional calculus with numerical methods for solving fractional order integral equations, integro-differential equations, and fractional order algebraic equations. Devised numerical methods are used in solving problems in different areas of engineering and sciences.
Multivariate Kernel Smoothing and Its Applications
Kernel smoothing has greatly evolved since its inception to become an essential methodology in the Data Science tool kit for the 21st century. Its widespread adoption is due to its fundamental role for multivariate exploratory data analysis, as well as the crucial role it plays in composite solutions to complex data challenges.
Pluses and Minuses
A guide to changing how you think about numbers and mathematics, from the prodigy changing the way the world thinks about math. We all know math is important: we live in the age of big data, our lives are increasingly governed by algorithms, and we're constantly faced with a barrage of statistics about everything from politics to our health. But what might be less obvious is how math factors into your daily life, and what memorizing all of those formulae in school had to do with it. Math prodigy Stefan Buijsman is beginning to change that through his pioneering research into the way we learn math. Plusses and Minuses is based in the countless ways that math is engrained in our daily lives, and shows readers how math can actually be used to make problems easier to solve. Taking readers on a journey around the world to visit societies that have developed without the use of math, and back into history to learn how and why various disciples of mathematics were invented, Buijsman shows the vital importance of math, and how a better understanding of mathematics will give us a better understanding of the world as a whole. Stefan Buijsman has become one of the most sought-after experts in math education after he completed his PhD at age 20. In Plusses and Minuses, he puts his research into practice to help anyone gain a better grasp of mathematics than they have ever had.
Analytische Probleme
Die Numerische Mathematik ist einer der Grundpfeiler des Mathematik-, Ingenieur-, Physik- und Informatikstudiums. Dieses zweib瓣ndige Lehrbuch ist f羹r Einf羹hrungsvorlesungen konzipiert und legt eine solide Basis f羹r weiterf羹hrende Lerneinheiten. Der Text ist aus Vorlesungsmanuskripten hervorgegangen, die der Verfasser seit etwa 30 Jahren f羹r seine Grundvorlesungen auf dem Gebiet der Numerischen Mathematik und des Wissenschaftlichen Rechnens an der Friedrich-Schiller-Universit瓣t Jena verwendet. Das Buch deckt den gesamten Bereich der Numerischen Mathematik von den klassischen Techniken wie Gau?scher Algorithmus und Newtonsches Verfahren bis hin zu modernen Algorithmen wie kubische Spline-Interpolation, Kleinste-Quadrate-Approximation mittels Householder- und Givens-Transformationen sowie Deflationstechniken ab. Die Verfahren werden mathematisch exakt beschrieben, in MATLAB-Codes implementiert und anhand von Beispielen demonstriert. Die MATLAB-Codes sind auf der Webseite des Verlages zum Download bereitgestellt, so dass der Leser seine eigenen Experimente mit den numerischen Verfahren durchf羹hren kann. Durch seinen didaktischen Aufbau und die zahlreichen anschaulichen Beispiele und ?bungsaufgaben eignet sich dieses Buch hervorragend als vorlesungsbegleitende Lekt羹re und als Grundlage f羹r ein erfolgreiches Selbststudium. Gleichzeitig kann es von Mathematikern, Naturwissenschaftlern und Ingenieuren als profundes Nachschlagewerk herangezogen werden. Mit der 4. Auflage wurde das umfangreiche Standardwerk der Numerischen Mathematik so in zwei B瓣nde aufgeteilt, dass diese relativ unabh瓣ngig voneinander gelesen werden k繹nnen. An vielen Stellen wurde der Text 羹berarbeitet und erg瓣nzt. Das betrifft insbesondere diejenigen Abschnitte, die f羹r Lehrerstudenten relevant sind sowie die Implementierung der numerischen Verfahren in der Programmiersprache MATLAB.
Bayesian Inference for Partially Identified Models
This book shows how the Bayesian approach to inference is applicable to partially identified models (PIMs) and examines the performance of Bayesian procedures in partially identified contexts. Drawing on his many years of research in this area, the author presents a thorough overview of the statistical theory, properties, and applications of PIM
Cyclic and Computer Generated Designs
The book is primarily concerned with the construction and analysis of designs with a number of different blocking structures, such as revolvable designs, row-column designs, and Latinized designs.
Improving Efficiency by Shrinkage
Offers a treatment of different kinds of James-Stein and ridge regression estimators from a frequentist and Bayesian point of view. The book explains and compares estimators analytically as well as numerically and includes Mathematica and Maple programs used in numerical comparison.;College or university bookshops may order five or more copies at a
Nonparametric Regression and Spline Smoothing
Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for co
Advanced Bayesian Methods for Medical Test Accuracy
After a review of the usual measures, including specificity, sensitivity, positive predictive value, negative predictive value, and the area under the ROC curve, this book expands its scope to cover the more advanced topics of verification bias, diagnostic tests with imperfect gold standards, and medical tests where no gold standard is available
An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space
General Notation.- 1 Prologue: The Algebraic Approach to Quantum Theories.- 2 ∗-Algebras.- 3 O*-Algebras.- 4 ∗-Representations.- 5 Positive Linear Functionals.- 6 Representations of Tensor Algebras.- 7 Integrable Representations of Commutative ∗-Algebras.- 8 The Weyl Algebra and the Canonical Commutation Relation.- 9 Integrable Representations of Enveloping Algebras.- 10 Archimedean Quadratic Modules and Positivstellens瓣tze.- 11 The Operator Relation XX*=F(X*X).- 12 Induced ∗-Representations.- 13 Well-behaved ∗-Representations.- 14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space.- B C*-Algebras and Representations.- C Locally Convex Spaces and Separation of Convex Sets.- References.- Symbol Index.- Subject Index.
Mild Differentiability Conditions for Newton’s Method in Banach Spaces
In this book the authors use a technique based on recurrence relations to study the convergence of the Newton method under mild differentiability conditions on the first derivative of the operator involved. The authors' technique relies on the construction of a scalar sequence, not majorizing, that satisfies a system of recurrence relations, and guarantees the convergence of the method. The application is user-friendly and has certain advantages over Kantorovich's majorant principle. First, it allows generalizations to be made of the results obtained under conditions of Newton-Kantorovich type and, second, it improves the results obtained through majorizing sequences. In addition, the authors extend the application of Newton's method in Banach spaces from the modification of the domain of starting points. As a result, the scope of Kantorovich's theory for Newton's method is substantially broadened. Moreover, this technique can be applied to any iterative method. This book is chiefly intended for researchers and (postgraduate) students working on nonlinear equations, as well as scientists in general with an interest in numerical analysis.
Statistical Methods for Environmental and Agricultural Sciences
The book emphasizes the practical application of statistics and provides examples in various fields of environmental and agriculture sciences.
What Makes Variables Random
What Makes Variables Random: Probability for the Applied Researcher provides an introduction to the foundations of probability that underlie the statistical analyses used in applied research. By explaining probability in terms of measure theory, it gives the applied researchers a conceptual framework to guide statistica
Advances on Theoretical and Methodological Aspects of Probability and Statistics
At the International Indian Statistical Association Conference, held at McMaster University in Ontario, Canada, participants focused on advancements in theory and methodology of probability and statistics. This is one of two volumes containing invited papers from the meeting. The 32 chapters deal with different topics of interest, including stochas
Numerical Linear Algebra
Many students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.
Markov Chains
This 2nd edition is a thoroughly revised and augmented version of the book with the same title published in 1999. The author begins with the elementary theory of Markov chains and very progressively brings the reader to more advanced topics. He gives a useful review of probability, making the book self-contained, and provides an appendix with detailed proofs of all the prerequisites from calculus, algebra, and number theory. A number of carefully chosen problems of varying difficulty are proposed at the close of each chapter, and the mathematics is slowly and carefully developed, in order to make self-study easier. The book treats the classical topics of Markov chain theory, both in discrete time and continuous time, as well as connected topics such as finite Gibbs fields, nonhomogeneous Markov chains, discrete-time regenerative processes, Monte Carlo simulation, simulated annealing, and queuing theory.The main additions of the 2nd edition are the exact sampling algorithm of Propp and Wilson, the electrical network analogy of symmetric random walks on graphs, mixing times and additional details on the branching process. The structure of the book has been modified in order to smoothly incorporate this new material. Among the features that should improve reader-friendliness, the three main ones are: a shared numbering system for the definitions, theorems and examples; the attribution of titles to the examples and exercises; and the blue highlighting of important terms. The result is an up-to-date textbook on stochastic processes. Students and researchers in operations research and electrical engineering, as well as in physics and biology, will find it very accessible and relevant.
Noninferiority Testing in Clinical Trials
Requiring no prior knowledge of NI testing, this book explains how to choose the NI margin as a small fraction of the therapeutic effect of the active control in a clinical trial. It discusses issues with estimating the effect size based on historical placebo control trials of the active control. The author covers basic concepts related to NI tr
Survey Sampling
Since publication of the first edition in 1992, the field of survey sampling has grown considerably. The new edition of Survey Sampling: Theory and Methods was updated to include recent research and newer methods. The authors undertook the daunting task of surveying the sampling literature of the past few decades to provide an outstanding research
Basic Statistics and Pharmaceutical Statistical Applications
This popular text covers statistical topics most relevant to those in the pharmaceutical industry and pharmacy practice. It focuses on the fundamentals required to understand descriptive and inferential statistics for problem solving. Incorporating new material in virtually every chapter, this third edition now provides information on software a
Handbook of Statistical Methods for Case-Control Studies
This handbook provides an in-depth treatment of up-to-date and currently developing statistical methods for the design and analysis of case-control studies, with a primary focus on case-control studies in epidemiology. Authors will be encouraged to illustrate the statistical methods they describe by application to datasets that are either alread
Generalized Sylvester Equations
This book presents a unified parametric approach for solving various types of GSEs. In an extremely neat and elegant matrix form, the author provides one unified parametric solution formula for the GSEs, which further reduces to a specific clear vector form when the parameter matrix F in the equations is a Jordan matrix. The book covers s
Introduction to Multivariate Analysis
This text shows how to use multivariate analysis to extract useful information from multivariate data and understand the structure of random phenomena. Along with the basic concepts of various procedures in traditional multivariate analysis, the book covers nonlinear techniques for clarifying phenomena behind observed multivariate data. It prima
Interval-Censored Time-To-Event Data
A practical guide for biomedical researchers, clinicians, biostatisticians, and graduate students in biostatistics, this volume covers the latest developments in the analysis and modeling of interval-censored time-to-event data. Top researchers from academia, biopharmaceutical industries, and government agencies show how up-to-date statistical m
Understanding Randomness
This concise, easy-to-follow book stimulates interest and develops proficiency in statistical analysis.
Geometric Aspects of Functional Analysis
Continuing the theme of the previous volumes, these seminar notes reflect general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. Two classical topics represented are the Concentration of Measure Phenomenon in the Local Theory of Banach Spaces, which has recently had triumphs in Random Matrix Theory, and the Central Limit Theorem, one of the earliest examples of regularity and order in high dimensions. Central to the text is the study of the Poincar矇 and log-Sobolev functional inequalities, their reverses, and other inequalities, in which a crucial role is often played by convexity assumptions such as Log-Concavity. The concept and properties of Entropy form an important subject, with Bourgain's slicing problem and its variants drawing much attention. Constructions related to Convexity Theory are proposed and revisited, as well as inequalities that go beyond the Brunn-Minkowski theory. One of the major current research directions addressedis the identification of lower-dimensional structures with remarkable properties in rather arbitrary high-dimensional objects. In addition to functional analytic results, connections to Computer Science and to Differential Geometry are also discussed.
Uncertainty Analysis of Experimental Data with R
This book covers methods for evaluation of experimental data commonly encountered in science and engineering. Measurements of quantities that vary in a continuous fashion, cannot be measured exactly; it is of interest to be able to quantify these uncertainties. The book centers around using the (free) software package R.
Handbook of Stochastic Analysis and Applications
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Exponential Distribution
The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the exponential distribution. Discussions include exponential regression, models and applications of mixtures, and applications to survival analysis.
An Introduction to Boundary Element Methods
This book describes the derivation of some fundamental solutions which in themselves are very helpful and valuable to lay the foundation for the theory of boundary element methods. It examines the two-dimensional potential problems, involving the Laplace and the Poisson equations.
Adjoint Equations and Perturbation Algorithms in Nonlinear Problems
This book presents the theory of adjoint equations in nonlinear problems and their applications to perturbation algorithms for solution of nonlinear problems in mathematical physics. It formulates a series of principles of construction of adjoint operators in nonlinear problems.
Mathematical Programming
This book serves as an introductory text in mathematical programming and optimization for students having a mathematical background that includes one semester of linear algebra and a complete calculus sequence. It includes computational examples to aid students develop computational skills.
Mathematical and Numerical Approaches for Multi-Wave Inverse Problems
Numerical Linear Algebra
Many students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.
Engineering Mathematics with Applications to Fire Engineering
This book addresses the need to have an engineering mathematics book focused at fire engineering. It includes review of the basic mathematical concepts followed by discussion of important concepts like transposing equations, forming a key part of engineering solutions.
Handbook of Industrial Engineering Equations, Formulas, and Calculations
Industrial engineering practitioners don't have to be computational experts. They just have to know where to get the computational resources that they need. This book provides access to computational resources needed by industrial engineers. It consists of several sections that each focus on a particular specialization area of industrial enginee
The Radon Transform and Local Tomography
This book serves as an introduction to the basic properties of the Radon transform. It presents a theory that deals with the study of the singularities of the Radon transform and its applications to the imaging in tomography, in a self-contained and systematic way.
Handbook of Discrete-Valued Time Series
Model a Wide Range of Count Time Series Handbook of Discrete-Valued Time Series presents state-of-the-art methods for modeling time series of counts and incorporates frequentist and Bayesian approaches for discrete-valued spatio-temporal data and multivariate data. While the book focuses on time series of counts, some of the techniques discussed can be applied to other types of discrete-valued time series, such as binary-valued or categorical time series.Explore a Balanced Treatment of Frequentist and Bayesian Perspectives Accessible to graduate-level students who have taken an elementary class in statistical time series analysis, the book begins with the history and current methods for modeling and analyzing univariate count series. It next discusses diagnostics and applications before proceeding to binary and categorical time series. The book then provides a guide to modern methods for discrete-valued spatio-temporal data, illustrating how far modern applications have evolved from their roots. The book ends with a focus on multivariate and long-memory count series.Get Guidance from Masters in the FieldWritten by a cohesive group of distinguished contributors, this handbook provides a unified account of the diverse techniques available for observation- and parameter-driven models. It covers likelihood and approximate likelihood methods, estimating equations, simulation methods, and a Bayesian approach for model fitting.
