Accelerated Life Testing of One-Shot Devices
Provides authoritative guidance on statistical analysis techniques and inferential methods for one-shot device life-testing Estimating the reliability of one-shot devices--electro-expolsive devices, fire extinguishers, automobile airbags, and other units that perform their function only once--poses unique analytical challenges to conventional approaches. Due to how one-shot devices are censored, their precise failure times cannot be obtained from testing. The condition of a one-shot device can only be recorded at a specific inspection time, resulting in a lack of lifetime data collected in life-tests. Accelerated Life Testing of One-shot Devices: Data Collection and Analysis addresses the fundamental issues of statistical modeling based on data collected from accelerated life-tests of one-shot devices. The authors provide inferential methods and procedures for planning accelerated life-tests, and describe advanced statistical techniques to help reliability practitioners overcome estimation problems in the real world. Topics covered include likelihood inference, competing-risks models, one-shot devices with dependent components, model selection, and more. Enabling readers to apply the techniques to their own lifetime data and arrive at the most accurate inference possible, this practical resource: Provides expert guidance on comprehensive data analysis of one-shot devices under accelerated life-tests Discusses how to design experiments for data collection from efficient accelerated life-tests while conforming to budget constraints Helps readers develops optimal designs for constant-stress and step-stress accelerated life-tests, mainstream life-tests commonly used in reliability practice Includes R code in each chapter for readers to use in their own analyses of one-shot device testing data Features numerous case studies and practical examples throughout Highlights important issues, problems, and future research directions in reliability theory and practice Accelerated Life Testing of One-shot Devices: Data Collection and Analysis is essential reading for graduate students, researchers, and engineers working on accelerated life testing data analysis.
Data Science in Theory and Practice
DATA SCIENCE IN THEORY AND PRACTICE EXPLORE THE FOUNDATIONS OF DATA SCIENCE WITH THIS INSIGHTFUL NEW RESOURCE Data Science in Theory and Practice delivers a comprehensive treatment of the mathematical and statistical models useful for analyzing data sets arising in various disciplines, like banking, finance, health care, bioinformatics, security, education, and social services. Written in five parts, the book examines some of the most commonly used and fundamental mathematical and statistical concepts that form the basis of data science. The authors go on to analyze various data transformation techniques useful for extracting information from raw data, long memory behavior, and predictive modeling. The book offers readers a multitude of topics all relevant to the analysis of complex data sets. Along with a robust exploration of the theory underpinning data science, it contains numerous applications to specific and practical problems. The book also provides examples of code algorithms in R and Python and provides pseudo-algorithms to port the code to any other language. Ideal for students and practitioners without a strong background in data science, readers will also learn from topics like: Analyses of foundational theoretical subjects, including the history of data science, matrix algebra and random vectors, and multivariate analysis A comprehensive examination of time series forecasting, including the different components of time series and transformations to achieve stationarity Introductions to both the R and Python programming languages, including basic data types and sample manipulations for both languages An exploration of algorithms, including how to write one and how to perform an asymptotic analysis A comprehensive discussion of several techniques for analyzing and predicting complex data sets Perfect for advanced undergraduate and graduate students in Data Science, Business Analytics, and Statistics programs, Data Science in Theory and Practice will also earn a place in the libraries of practicing data scientists, data and business analysts, and statisticians in the private sector, government, and academia.
Sous-titrage automatique des images
L'automatisation du sous-titrage, c'est-?-dire la cr矇ation de la description linguistique d'une image ? l'aide de n'importe quel traitement du langage naturel, est une t璽che difficile. Il faut avoir une bonne ma簾trise du traitement de l'image et du traitement du langage naturel. Ce livre traite des diff矇rentes techniques disponibles qui servent de mod癡le pour le sous-titrage des images. Les progr癡s de la technologie en termes de reconnaissance d'objets et d'apprentissage machine ont beaucoup am矇lior矇 les performances du mod癡le de sous-titrage d'images ces derni癡res ann矇es. En plus de cela, nous allons essayer d'aborder les diff矇rentes techniques et algorithmes pour construire ce mod癡le. En fin de compte, l'矇valuation du mod癡le joue un r繫le important qui sera utile pour d矇terminer quel algorithme convient le mieux au sc矇nario. Il existe des techniques qui peuvent 礙tre utilis矇es pour 矇valuer les performances telles que la matrice de confusion, le f1-score mais dans ce cas, les donn矇es sont bas矇es sur le langage naturel donc sur le fait qu'il existe un certain type sp矇cial de technologie qui peut 礙tre utilis矇 comme Microsoft COCO et Flickr30K.
Beta Thalassemia - A Data Analytics Perspective
The work entails a novel approach towards realizing distribution of Thalassemia medical records based on Age, Gender, Weight and Haemoglobin Level. It also indicates the rate of growth of thalassemia with corresponding sex bifurcation. The total number of blood transfusions with respect to ferritin, frequency (In months), Height, weight, eco have been analysed based on the graphical representation. The work points out a Statistical Assessment of Health Related Quality of Life in Pediatric Patients with Beta-Thalassaemia. Posterior Distribution Characterization for Pairwise Correlations for Baseline and 3 Months has been carried out based on Log Likelihood Function, Prior Distribution, and Posterior Distribution. In case of posterior distribution for Bayesian correlation, a bell shaped curve is observed. This work highlights an Analysis of Beta-Thalassemia Patients' prognosis in the light of Radial Basis function and non-parametric test.
Effective Statistical Learning Methods for Actuaries II
This book summarizes the state of the art in tree-based methods for insurance: regression trees, random forests and boosting methods. It also exhibits the tools which make it possible to assess the predictive performance of tree-based models. Actuaries need these advanced analytical tools to turn the massive data sets now at their disposal into opportunities. The exposition alternates between methodological aspects and numerical illustrations or case studies. All numerical illustrations are performed with the R statistical software. The technical prerequisites are kept at a reasonable level in order to reach a broad readership. In particular, master's students in actuarial sciences and actuaries wishing to update their skills in machine learning will find the book useful. This is the second of three volumes entitled Effective Statistical Learning Methods for Actuaries. Written by actuaries for actuaries, this series offers a comprehensive overview of insurancedata analytics with applications to P&C, life and health insurance.
Using Mathematics to Understand Biological Complexity
1. Collaborative Workshop for Women in Mathematical Biology (R. Segal, B. Shtylla, S. Sindi).- 2. Connecting Actin Polymer Dynamics Across Multiple Scales (C. Copos, B. Bannish, K. Gasior, R.L. Pinals, M.W. Rostami, A.T. Dawes).- 3. Modeling RNA: DNA Hybrids with Formal Grammars (N. Jonoska, N. Obatake, S. Poznanovic, C. Price, M. Riehl, M. Vazquez).- 4. Secondary Structure Ensemble Analysis via Community Detection (H. Du, M.M. Ferrari, C. Heitsch, F. Hurley, C.V. Mennicke, B.D. Sullivan, and B. Xu.)- 5. How Do Interventions Impact Malaria Dynamics Between Neighboring Countries? A Case Study with Botswana and Zimbabwe (F. Agusto, A. Goldberg, O. Ortega, Joan Ponce+, Sofya Zaytseva, S. Sindi, Sally Blower).- 6. Investigating the Impact of Combination Phage and Antibiotic Therapy (S. Banuelos, H. Gulbudak, M.A. Horn, Q. Huang, A. Nandi, H Ryu, R. Segal).- 7. Mathematical Modeling of Retinal Degeneration (E. Camacho, A. Dobreva, K. Larripa, A. Radulescu, D. Schmidt, I. Trejo).- 8. A Framework for Performing Data-Driven Modeling of Tumor Growth with Radiotherapy Treatment (H. Cho, A.L. Lewis, K.M. Storey, R. Jennings, B. Shtylla, A.M. Reynolds, H.M. Byrne).
Density Evolution Under Delayed Dynamics
This monograph has arisen out of a number of attempts spanning almost five decades to understand how one might examine the evolution of densities in systems whose dynamics are described by differential delay equations. Though the authors have no definitive solution to the problem, they offer this contribution in an attempt to define the problem as they see it, and to sketch out several obvious attempts that have been suggested to solve the problem and which seem to have failed. They hope that by being available to the general mathematical community, they will inspire others to consider-and hopefully solve-the problem. Serious attempts have been made by all of the authors over the years and they have made reference to these where appropriate.
The Applications Of Elliptic Functions
Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.
Fundamentals of Environmental Discharge Modeling
This book examines engineering and mathematical models for documenting and approving mechanical and environmental discharges. The author emphasizes engineering design considerations as well as applications to waste water and atmospheric discharges.Chapters discuss: the fundamentals of turbulent jet mixing, dilution concepts, and mixing zone conceptsdiffuser configurations and head loss calculationsdifferent modeling techniques and accepted models - discussed in detail with theoretical background, restrictions, input, output, and examplesLagrangian and the EPA UM 2-dimensional diffuser modelthe PLUMES interfaceEulerian integral methods, EPA UDKHG 3-dimensional diffuser model, and PDSG surface discharge modelempirical techniques, RSB diffuser model, the CORMIX family of models for both diffusers and surface dischargenumerical methods with a discussion of shelf commercial modelsGaussian atmospheric plume modelsFundamentals of Environmental Discharge Modeling includes numerous case studies and examples for each model and problem.
An Introduction to C*-Algebras and the Classification Program
This book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras.The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
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
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.
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.
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.
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
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
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.
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
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
Circular and Linear Regression
Exploring the recent achievements that have occurred since the mid-1990s, this book explains how to use modern algorithms to fit geometric contours to observed data in image processing and computer vision. The author covers all facets-geometric, statistical, and computational-of the methods. He looks at how the numerical algorithms relate to one
Missing and Modified Data in Nonparametric Estimation
The book gives a unified approach to nonparametric curve estimation based on missing and modified data. Missing data includes cases of missing at random and missing not at random, while data modification includes truncation and censoring, typical in survival analysis, as well as measurement errors and amplitude modulation. A universal nonparamet
Linear Models and the Relevant Distributions and Matrix Algebra
Using linear statistical models as a basis for statistical inference and the theoretical underpinnings of resultant inferential procedures. Includes topics typically covered less extensively; prediction, multiple-comparison procedures for controlling FDR, spherical/elliptical distributions.
Essentials of a Successful Biostatistical Collaboration
The aim of this book is to equip biostatisticians and other quantitative scientists with the necessary skills, knowledge, and habits to collaborate effectively with clinicians in the healthcare field. The book provides valuable insight on where to look for information and material on sample size and statistical techniques commonly used in clinic
Robust Regression
Robust Regression: Analysis and Applications characterizes robust estimators in terms of how much they weigh.
Measures of Interobserver Agreement and Reliability
Exploring applications in medical research and clinical epidemiology, this text continues to cover important issues related to the design and analysis of reliability and agreement studies. This edition contains a new chapter that describes various models for methods comparison studies as well as a new chapter on the analysis of reproducibility u
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.
Models for Dependent Time Series
This book addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. It shows how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data. The book presents several extensions to the standard autoregressive mo
Truncated and Censored Samples
This book deals with the development of methodology for the analysis of truncated and censored sample data. It is primarily intended as a handbook for practitioners who need simple and efficient methods for the analysis of incomplete sample data.
Randomization Tests
Building on the previous editions that have served as standard textbooks and references for more than twenty-five years, Randomization Tests, Fourth Edition describes the randomization test theory, clarifies the hypotheses being tested, and discusses the role of random assignment. This edition also features updated material on N-of-1 randomi
A Course on Tug-Of-War Games with Random Noise
1 Introduction.- 2 The linear case: random walk and harmonic functions.- 3 Tug-of-War with noise. Case p ∈ [2,∞).- 4 Boundary aware tug-of-war with noise. Case p ∈ (2,∞).- 5 Game-regularity and convergence. Case p ∈ (2,∞).- 6 Mixed tug-of-war with noise. Case p ∈ (1,∞).- A Background in probability.- B Background in Brownian motion.- C Background in PDEs. D Solutions to selected exercises.- References.- Index.
Statistical Inference Based on Divergence Measures
Organized in systematic way, Statistical Inference Based on Divergence Measures presents classical problems of statistical inference, such as estimation and hypothesis testing, on the basis of measures of entropy and divergence with applications to multinomial and generation populations. On the basis of divergence measures, this book introduces min
Handbook of Adaptive Designs in Pharmaceutical and Clinical Development
This handbook provides a comprehensive and unified presentation of the principles and latest statistical methodologies used when modifying trial procedures based on accrued data of ongoing clinical trials. The book also gives a well-balanced summary of current regulatory perspectives and presents real-world examples of a range of adaptive design
Skew-Elliptical Distributions and Their Applications
Reviewing advances in skew-elliptical distributions, this book collates developments, theory, results and applications in a single source, discussing theory and inference for skew-elliptical distribution, and examining applications and case studies.
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.
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.
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.
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
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
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
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.
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.
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.
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.
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
