This book is intended for use in advanced graduate courses in statistics / machine learning, as well as for all experimental neuroscientists seeking to understand statistical methods at a deeper level, and theoretical neuroscientists with a limited background in statistics. It reviews almost all areas of applied statistics, from basic statistical estimation and test theory, linear and nonlinear approaches for regression and classification, to model selection and methods for dimensionality reduction, density estimation and unsupervised clustering. Its focus, however, is linear and nonlinear time series analysis from a dynamical systems perspective, based on which it aims to convey an understanding also of the dynamical mechanisms that could have generated observed time series. Further, it integrates computational modeling of behavioral and neural dynamics with statistical estimation and hypothesis testing. This way computational models in neuroscience are not only explanatory frameworks, but become powerful, quantitative data-analytical tools in themselves that enable researchers to look beyond the data surface and unravel underlying mechanisms. Interactive examples of most methods are provided through a package of MatLab routines, encouraging a playful approach to the subject, and providing readers with a better feel for the practical aspects of the methods covered. "Computational neuroscience is essential for integrating and providing a basis for understanding the myriads of remarkable laboratory data on nervous system functions. Daniel Durstewitz has excellently covered the breadth of computational neuroscience from statistical interpretations of data to biophysically based modeling of the neurobiological sources of those data. His presentation is clear, pedagogically sound, and readily useable by experts and beginners alike. It is a pleasure to recommend this very well crafted discussion to experimental neuroscientists as well as mathematically well versed Physicists. The book acts as a window to the issues, to the questions, and to the tools for finding the answers to interesting inquiries about brains and how they function." Henry D. I. Abarbanel Physics and Scripps Institution of Oceanography, University of California, San Diego "This book delivers a clear and thorough introduction to sophisticated analysis approaches useful in computational neuroscience. The models described and the examples provided will help readers develop critical intuitions into what the methods reveal about data. The overall approach of the book reflects the extensive experience Prof. Durstewitz has developed as a leading practitioner of computational neuroscience. " Bruno B. Averbeck

Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is a self-contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queuing theory and stochastic modeling and include M/G/1 and GI/M/1-type Markov chain, quasi-birth-death processes, non-skip free queues and tree-like stochastic processes. Written for applied probabilists and numerical analysts, but accessible to engineers and scientists working on telecommunications and evaluation of computer systems performances, it provides a systematic treatment of the theory and algorithms for important families of structured Markov chains and a thorough overview of the current literature. The book, consisting of nine Chapters, is presented in three parts. Part 1 covers a basic description of the fundamental concepts related to Markov chains, a systematic treatment of the structure matrix tools, including finite Toeplitz matrices, displacement operators, FFT, and the infinite block Toeplitz matrices, their relationship with matrix power series and the fundamental problems of solving matrix equations and computing canonical factorizations. Part 2 deals with the description and analysis of structure Markov chains and includes M/G/1, quasi-birth-death processes, non-skip-free queues and tree-like processes. Part 3 covers solution algorithms where new convergence and applicability results are proved. Each chapter ends with bibliographic notes for further reading, and the book ends with an appendix collecting the main general concepts and results used in the book, a list of the main annotations and algorithms used in the book, and an extensive index.

This book is a comprehensive guide to extreme value theory in engineering. Written for the end user with intermediate and advanced statistical knowledge, it covers classical methods as well as recent advances. A collection of 150 examples illustrates the theoretical results and takes the reader from simple applications through complex cases of dependence.

This edited volume is a definitive text on adaptive clinical trial designs from creation and customization to utilization. As this book covers the full spectrum of topics involved in the adaptive designs arena, it will serve as a valuable reference for researchers working in industry, government and academia. The target audience is anyone involved in the planning and execution of clinical trials, in particular, statisticians, clinicians, pharmacometricians, clinical operation specialists, drug supply managers, and infrastructure providers. In spite of the increased efficiency of adaptive trials in saving costs and time, ultimately getting drugs to patients sooner, their adoption in clinical development is still relatively low. One of the chief reasons is the higher complexity of adaptive design trials as compared to traditional trials. Barriers to the use of clinical trials with adaptive features include the concerns about the integrity of study design and conduct, the risk of regulatory non-acceptance, the need for an advanced infrastructure for complex randomization and clinical supply scenarios, change management for process and behavior modifications, extensive resource requirements for the planning and design of adaptive trials and the potential to relegate key decision makings to outside entities. There have been limited publications that address these practical considerations and recommend best practices and solutions. This book fills this publication gap, providing guidance on practical considerations for adaptive trial design and implementation. The book comprises three parts: Part I focuses on practical considerations from a design perspective, whereas Part II delineates practical considerations related to the implementation of adaptive trials. Putting it all together, Part III presents four illustrative case studies ranging from description and discussion of specific adaptive trial design considerations to the logistic and regulatory issues faced in trial implementation.

Bringing together the expertise of leading key opinion leaders from pharmaceutical industry, academia, and regulatory agencies, this book provides a balanced and comprehensive coverage of practical considerations for adaptive trial design and implementation.

This book studies the brilliant Danish 19th Century astronomer, T.N. Thiele who made important contributions to statistics, actuarial science, astronomy and mathematics. The most important of these contributions in statistics are translated into English for the first time, and the text includes comments that set his achievements in a modern and historical perspective.

This richly illustrated book provides an overview of the design and analysis of experiments with a focus on non-clinical experiments in the life sciences, including animal research. It covers the most common aspects of experimental design such as handling multiple treatment factors and improving precision. In addition, it addresses experiments with large numbers of treatment factors and response surface methods for optimizing experimental conditions or biotechnological yields. The book emphasizes the estimation of effect sizes and the principled use of statistical arguments in the broader scientific context. It gradually transitions from classical analysis of variance to modern linear mixed models, and provides detailed information on power analysis and sample size determination, including 'portable power' formulas for making quick approximate calculations. In turn, detailed discussions of several real-life examples illustrate the complexities and aberrations that can arise in practice. Chiefly intended for students, teachers and researchers in the fields of experimental biology and biomedicine, the book is largely self-contained and starts with the necessary background on basic statistical concepts. The underlying ideas and necessary mathematics are gradually introduced in increasingly complex variants of a single example. Hasse diagrams serve as a powerful method for visualizing and comparing experimental designs and deriving appropriate models for their analysis. Manual calculations are provided for early examples, allowing the reader to follow the analyses in detail. More complex calculations rely on the statistical software R, but are easily transferable to other software. Though there are few prerequisites for effectively using the book, previous exposure to basic statistical ideas and the software R would be advisable.

This volume is a unique combination of papers that cover critical topics in biostatistics from academic, government, and industry perspectives. The 6 sections cover Bayesian methods in biomedical research; Diagnostic medicine and classification; Innovative Clinical Trials Design; Modelling and Data Analysis; Personalized Medicine; and Statistical Genomics. The real world applications are in clinical trials, diagnostic medicine and genetics. The peer-reviewed contributions were solicited and selected from some 400 presentations at the annual meeting of the International Chinese Statistical Association (ICSA), held with the International Society for Biopharmaceutical Statistics (ISBS). The conference was held in Bethesda in June 2013, and the material has been subsequently edited and expanded to cover the most recent developments.

This book walks you through learning probability and statistics from a Bayesian point of view. From an introduction to probability theory through to frameworks for doing rigorous calculations of probability, it discusses Bayes' Theorem before illustrating how to use it in a variety of different situations with data addressing social and psychological issues. The book also: Equips you with coding skills in the statistical modelling language Stan and programming language R. Discusses how Bayesian approaches to statistics compare to classical approaches. Introduces Markov Chain Monte Carlo methods for doing Bayesian statistics through computer simulations, so you understand how Bayesian solutions are implemented. Features include an introduction to each chapter and a chapter summary to help you check your learning. All the examples and data used in the book are also available in the online resources so you can practice at your own pace. For readers with some understanding of basic mathematical functions and notation, this book will get you up and running so you can do Bayesian statistics with confidence.

This book presents the principles and methods for the practical analysis and prediction of economic and financial time series. It covers decomposition methods, autocorrelation methods for univariate time series, volatility and duration modeling for financial time series, and multivariate time series methods, such as cointegration and recursive state space modeling. It also includes numerous practical examples to demonstrate the theory using real-world data, as well as exercises at the end of each chapter to aid understanding. This book serves as a reference text for researchers, students and practitioners interested in time series, and can also be used for university courses on econometrics or computational finance.

The author's previous book, Random Walk in Random and Non-Random Environments, was devoted to the investigation of the Brownian motion of a simple particle. The present book studies the independent motions of infinitely many particles in the d-dimensional Euclidean space Rd. In Part I the particles at time t = 0 are distributed in Rd according to the law of a given random field and they execute independent random walks. Part II is devoted to branching random walks, i.e. to the case where the particles execute random motions and birth and death processes independently. Finally, in Part III, functional laws of iterated logarithms are proved for the cases of independent motions and branching processes.

This textbook examines empirical linguistics from a theoretical linguist's perspective. It provides both a theoretical discussion of what quantitative corpus linguistics entails and detailed, hands-on, step-by-step instructions to implement the techniques in the field. The statistical methodology and R-based coding from this book teach readers the basic and then more advanced skills to work with large data sets in their linguistics research and studies. Massive data sets are now more than ever the basis for work that ranges from usage-based linguistics to the far reaches of applied linguistics. This book presents much of the methodology in a corpus-based approach. However, the corpus-based methods in this book are also essential components of recent developments in sociolinguistics, historical linguistics, computational linguistics, and psycholinguistics. Material from the book will also be appealing to researchers in digital humanities and the many non-linguistic fields that use textual data analysis and text-based sensorimetrics. Chapters cover topics including corpus processing, frequencing data, and clustering methods. Case studies illustrate each chapter with accompanying data sets, R code, and exercises for use by readers. This book may be used in advanced undergraduate courses, graduate courses, and self-study.

This book is a comprehensive introduction of the reader into the simulation and modelling techniques and their application in the management of organisations. The book is rooted in the thorough understanding of systems theory applied to organisations and focuses on how this theory can apply to econometric models used in the management of organisations. The econometric models in this book employ linear and dynamic programming, graph theory, queuing theory, game theory, etc. and are presented and analysed in various fields of application, such as investment management, stock management, strategic decision making, management of production costs and the lifecycle costs of quality and non-quality products, production quality Management, etc.

This volume collects selected, peer-reviewed contributions from the 2nd Conference of the International Society for Nonparametric Statistics (ISNPS), held in Cadiz (Spain) between June 11-16 2014, and sponsored by the American Statistical Association, the Institute of Mathematical Statistics, the Bernoulli Society for Mathematical Statistics and Probability, the Journal of Nonparametric Statistics and Universidad Carlos III de Madrid. The 15 articles are a representative sample of the 336 contributed papers presented at the conference. They cover topics such as high-dimensional data modelling, inference for stochastic processes and for dependent data, nonparametric and goodness-of-fit testing, nonparametric curve estimation, object-oriented data analysis, and semiparametric inference. The aim of the ISNPS 2014 conference was to bring together recent advances and trends in several areas of nonparametric statistics in order to facilitate the exchange of research ideas, promote collaboration among researchers from around the globe, and contribute to the further development of the field.

The book covers computational statistics, its methodologies and applications for IoT device. It includes the details in the areas of computational arithmetic and its influence on computational statistics, numerical algorithms in statistical application software, basics of computer systems, statistical techniques, linear algebra and its role in optimization techniques, evolution of optimization techniques, optimal utilization of computer resources, and statistical graphics role in data analysis. It also explores computational inferencing and computer model's role in design of experiments, Bayesian analysis, survival analysis and data mining in computational statistics.

This book illustrates the EU-wide Solvency II framework for the insurance industry, which was implemented on January 1, 2016, after a long project phase. Analogous to the system for banks, it is based on three pillars and the authors analyze the complete framework pillar by pillar with a consistent data model for a non-life insurer, which was developed by the Research Group Financial & Actuarial Risk Management (FaRis) at the Institute for Insurance Studies of the TH Koeln - University of Applied Sciences. The book leverages the long-standing and close cooperation between the University of Limerick (Ireland) and the Institute for Insurance Studies at TH Koeln - University of Applied Sciences (Germany).

This text presents a wide-ranging and rigorous overview of nearest neighbor methods, one of the most important paradigms in machine learning. Now in one self-contained volume, this book systematically covers key statistical, probabilistic, combinatorial and geometric ideas for understanding, analyzing and developing nearest neighbor methods. Gerard Biau is a professor at Universite Pierre et Marie Curie (Paris). Luc Devroye is a professor at the School of Computer Science at McGill University (Montreal).

This book reconsiders statistical methods from the point of view of entropy, and introduces entropy-based approaches for data analysis. Further, it interprets basic statistical methods, such as the chi-square statistic, t-statistic, F-statistic and the maximum likelihood estimation in the context of entropy. In terms of categorical data analysis, the book discusses the entropy correlation coefficient (ECC) and the entropy coefficient of determination (ECD) for measuring association and/or predictive powers in association models, and generalized linear models (GLMs). Through association and GLM frameworks, it also describes ECC and ECD in correlation and regression analyses for continuous random variables. In multivariate statistical analysis, canonical correlation analysis, T2-statistic, and discriminant analysis are discussed in terms of entropy. Moreover, the book explores the efficiency of test procedures in statistical tests of hypotheses using entropy. Lastly, it presents an entropy-based path analysis for structural GLMs, which is applied in factor analysis and latent structure models. Entropy is an important concept for dealing with the uncertainty of systems of random variables and can be applied in statistical methodologies. This book motivates readers, especially young researchers, to address the challenge of new approaches to statistical data analysis and behavior-metric studies.

This book presents the proceedings of the 2nd Pacific Rim Statistical Conference for Production Engineering: Production Engineering, Big Data and Statistics, which took place at Seoul National University in Seoul, Korea in December, 2016. The papers included discuss a wide range of statistical challenges, methods and applications for big data in production engineering, and introduce recent advances in relevant statistical methods.

This book introduces the basic fundamentals, models, emulators and analyses of mem-elements in the circuit theory with applications. The book starts reviewing the literature on mem-elements, models and their recent applications. It presents mathematical models, numerical results, circuit simulations, and experimental results for double-loop hysteresis behavior of mem-elements. The authors introduce a generalized memristor model in the fractional-order domain under different input and different designs for emulator-based mem-elements, with circuit and experimental results. The basic concept of memristive-based relaxation-oscillators in the circuit theory is also covered. The reader will moreover find in this book information on memristor-based multi-level digital circuits, memristor-based multi-level multiplier and memcapacitor-based oscillators and synaptic circuits.

In 1983 O.J. Boxma and the author have published a research monograph on Boundary Value Problems in Queueing System Analysis. The continuation of that research is described in the present monograph. The technique developed in the 1983-monograph has appeared to be quite powerful in the construction of explicit expressions for the generating functions and/or Laplace-Stieltjes transforms of characteristic distributions needed in the performance evaluation of stoachistic models stemming from computer system and telecommunication engineering. The book covers the following topics: One- Dimensional Random Walks; Two-Dimensional Random Walks; the Two-Dimensional Workload Process; and the N-Dimensional Random Walk.

The general topic of this book is the ergodic behavior of Markov processes. A detailed introduction to methods for proving ergodicity and upper bounds for ergodic rates is presented in the first part of the book, with the focus put on weak ergodic rates, typical for Markov systems with complicated structure. The second part is devoted to the application of these methods to limit theorems for functionals of Markov processes. The book is aimed at a wide audience with a background in probability and measure theory. Some knowledge of stochastic processes and stochastic differential equations helps in a deeper understanding of specific examples. Contents Part I: Ergodic Rates for Markov Chains and Processes Markov Chains with Discrete State Spaces General Markov Chains: Ergodicity in Total Variation MarkovProcesseswithContinuousTime Weak Ergodic Rates Part II: Limit Theorems The Law of Large Numbers and the Central Limit Theorem Functional Limit Theorems

The book includes articles from eminent international scientists discussing a wide spectrum of topics of current importance in mathematics and statistics and their applications. It presents state-of-the-art material along with a clear and detailed review of the relevant topics and issues concerned. The topics discussed include message transmission, colouring problem, control of stochastic structures and information dynamics, image denoising, life testing and reliability, survival and frailty models, analysis of drought periods, prediction of genomic profiles, competing risks, environmental applications and chronic disease control. It is a valuable resource for researchers and practitioners in the relevant areas of mathematics and statistics.

This proceedings volume features top contributions in modern statistical methods from Statistics 2021 Canada, the 6th Annual Canadian Conference in Applied Statistics, held virtually on July 15-18, 2021. Papers are contributed from established and emerging scholars, covering cutting-edge and contemporary innovative techniques in statistics and data science. Major areas of contribution include Bayesian statistics; computational statistics; data science; semi-parametric regression; and stochastic methods in biology, crop science, ecology and engineering. It will be a valuable edited collection for graduate students, researchers, and practitioners in a wide array of applied statistical and data science methods.

The articles in this collection are a sampling of some of the research presented during the conference "Stochastic Analysis and Related Topics", held in May of 2015 at Purdue University in honor of the 60th birthday of Rodrigo Banuelos. A wide variety of topics in probability theory is covered in these proceedings, including heat kernel estimates, Malliavin calculus, rough paths differential equations, Levy processes, Brownian motion on manifolds, and spin glasses, among other topics.

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.