The management of operational risk in the banking industry has undergone explosive changes over the last decade due to substantial changes in the operational environment. Globalization, deregulation, the use of complex financial products, and changes in information technology have resulted in exposure to new risks which are very different from market and credit risks. In response, the Basel Committee on Banking Supervision has developed a new regulatory framework for capital measurement and standards for the banking sector. This has formally defined operational risk and introduced corresponding capital requirements.

Many banks are undertaking quantitative modelling of operational risk using the Loss Distribution Approach (LDA) based on statistical quantification of the frequency and severity of operational risk losses. There are a number of unresolved methodological challenges in the LDA implementation. Overall, the area of quantitative operational risk is very new and different methods are under hot debate.

This book is devoted to quantitative issues in LDA. In particular, the use of Bayesian inference is the main focus. Though it is very new in this area, the Bayesian approach is well suited for modelling operational risk, as it allows for a consistent and convenient statistical framework for quantifying the uncertainties involved. It also allows for the combination of expert opinion with historical internal and external data in estimation procedures. These are critical, especially for low-frequency/high-impact operational risks.

This book is aimed at practitioners in risk management, academic researchers in financial mathematics, banking industry regulators and advanced graduate students in the area. It is a must-read for anyone who works, teaches or does research in the area of financial risk.

This book is an extension of the author's first book and serves as a guide and manual on how to specify and compute 2-, 3-, and 4-Event Bayesian Belief Networks (BBN). It walks the learner through the steps of fitting and solving fifty BBN numerically, using mathematical proof. The author wrote this book primarily for inexperienced learners as well as professionals, while maintaining a proof-based academic rigor. The author's first book on this topic, a primer introducing learners to the basic complexities and nuances associated with learning Bayes' theorem and inverse probability for the first time, was meant for non-statisticians unfamiliar with the theorem-as is this book. This new book expands upon that approach and is meant to be a prescriptive guide for building BBN and executive decision-making for students and professionals; intended so that decision-makers can invest their time and start using this inductive reasoning principle in their decision-making processes. It highlights the utility of an algorithm that served as the basis for the first book, and includes fifty 2-, 3-, and 4-event BBN of numerous variants.

"A First Course in Machine Learning by Simon Rogers and Mark Girolami is the best introductory book for ML currently available. It combines rigor and precision with accessibility, starts from a detailed explanation of the basic foundations of Bayesian analysis in the simplest of settings, and goes all the way to the frontiers of the subject such as infinite mixture models, GPs, and MCMC." -Devdatt Dubhashi, Professor, Department of Computer Science and Engineering, Chalmers University, Sweden "This textbook manages to be easier to read than other comparable books in the subject while retaining all the rigorous treatment needed. The new chapters put it at the forefront of the field by covering topics that have become mainstream in machine learning over the last decade." -Daniel Barbara, George Mason University, Fairfax, Virginia, USA "The new edition of A First Course in Machine Learning by Rogers and Girolami is an excellent introduction to the use of statistical methods in machine learning. The book introduces concepts such as mathematical modeling, inference, and prediction, providing 'just in time' the essential background on linear algebra, calculus, and probability theory that the reader needs to understand these concepts." -Daniel Ortiz-Arroyo, Associate Professor, Aalborg University Esbjerg, Denmark "I was impressed by how closely the material aligns with the needs of an introductory course on machine learning, which is its greatest strength...Overall, this is a pragmatic and helpful book, which is well-aligned to the needs of an introductory course and one that I will be looking at for my own students in coming months." -David Clifton, University of Oxford, UK "The first edition of this book was already an excellent introductory text on machine learning for an advanced undergraduate or taught masters level course, or indeed for anybody who wants to learn about an interesting and important field of computer science. The additional chapters of advanced material on Gaussian process, MCMC and mixture modeling provide an ideal basis for practical projects, without disturbing the very clear and readable exposition of the basics contained in the first part of the book." -Gavin Cawley, Senior Lecturer, School of Computing Sciences, University of East Anglia, UK "This book could be used for junior/senior undergraduate students or first-year graduate students, as well as individuals who want to explore the field of machine learning...The book introduces not only the concepts but the underlying ideas on algorithm implementation from a critical thinking perspective." -Guangzhi Qu, Oakland University, Rochester, Michigan, USA

Nonlinearity and stochastic structural dynamics is of common interest to engineers and applied scientists belonging to many disciplines. Recent research in this area has been concentrated on the response and stability of nonlinear mechanical and structural systems subjected to random escitation. Simultaneously the focus of research has also been directed towards understanding intrinsic nonlinear phenomena like bifurcation and chaos in deterministic systems. These problems demand a high degree of sophistication in the analytical and numerical approaches. At the same time they arise from considerations of nonlinear system response to turbulence, earthquacke, wind, wave and guidancy excitations. The topic thus attracts votaries of both analytical rigour and practical applications. This books gives important and latest developments in the field presenting in a coherent fashion the research findings of leading international groups working in the area of nonlinear random vibration and chaos.

This edited volume presents current research in biostatistics with emphasis on biopharmaceutical applications. Featuring contributions presented at the 2017 ICSA Applied Statistics Symposium held in Chicago, IL on June 25 to 28, 2017, this book explores timely topics that have a high potential impact on statistical methodology and future research in biostatistics and biopharmaceuticals. The theme of this conference was Statistics for a New Generation: Challenges and Opportunities, in recognition of the advent of a new generation of statisticians. The conference attracted statisticians working in academia, government, and industry; domestic and international statisticians. From the conference, the editors selected 28 high-quality presentations and invited the speakers to prepare full chapters for this book. These contributions are divided into four parts: Part I Biostatistical Methodology, Part II Statistical Genetics and Bioinformatics, Part III Regulatory Statistics, and Part IV Biopharmaceutical Research and Applications.Featuring contributions on topics such as statistics in genetics, bioinformatics, biostatistical methodology, and statistical computing, this book is beneficial to researchers, academics, practitioners and policy makers in biostatistics and biopharmaceuticals.

This book is devoted to an investigation of the basic problems of the the- ory of random fields which are characterized by certain singular properties (e. g., unboundedness, or vanishing) of their spectral densities. These ran- dom fields are called, the random fields with singular spectrum, long-memory fields, random fields with long-range dependence, fields with slowly decaying correlations or strongly dependent random fields by various authors. This phenomenon has been observed empirically by many scientists long before suitable mathematical models were known. The methods and results differ significantly from the theory of weakly dependent random fields. The first chapter presents basic concepts of the spectral theory of random fields, some examples of random processes and fields with singular spectrum, Tauberian and Abelian theorems for the covariance function of singular ran- dom fields. In the second chapter limit theorems for non-linear functionals of random fields with singular spectrum are proved. Chapter 3 summarizes some limit theorems for geometric functionals of random fields with long-range dependence. Limit distributions of the solutions of Burgers equation with random data via parabolic and hyperbolic rescaling are presented in chapter 4. And chapter 5 presents some problems of statistical analysis of random fields with singular spectrum. I would like to thank the editor, Michiel Hazewinkel, for his support. I am grateful to the following students and colleagues: 1. Deriev, A. Olenko, K. Rybasov, L. Sakhno, M. Sharapov, A. Sikorskii, M. Silac-BenSic. I would also like to thank V.Anh, O. Barndorff-Nielsen,Yu. Belyaev, P.

Lognormal distributions are one of the most commonly studied models in the sta tistical literature while being most frequently used in the applied literature. The lognormal distributions have been used in problems arising from such diverse fields as hydrology, biology, communication engineering, environmental science, reliability, agriculture, medical science, mechanical engineering, material science, and pharma cology. Though the lognormal distributions have been around from the beginning of this century (see Chapter 1), much of the work concerning inferential methods for the parameters of lognormal distributions has been done in the recent past. Most of these methods of inference, particUlarly those based on censored samples, involve extensive use of numerical methods to solve some nonlinear equations. Order statistics and their moments have been discussed quite extensively in the literature for many distributions. It is very well known that the moments of order statistics can be derived explicitly only in the case of a few distributions such as exponential, uniform, power function, Pareto, and logistic. In most other cases in cluding the lognormal case, they have to be numerically determined. The moments of order statistics from a specific lognormal distribution have been tabulated ear lier. However, the moments of order statistics from general lognormal distributions have not been discussed in the statistical literature until now primarily due to the extreme computational complexity in their numerical determination."

Characterising spatial and temporal variation in environmental properties, generatingmapsfromsparse samples,and quantifyinguncertaintiesin the maps,are key concerns across the environmental sciences. The body of tools known as g- statistics offers a powerful means of addressing these and related questions. This volume presents recent research in methodological developments in geostatistics and in a variety of speci?c environmental application areas including soil science, climatology, pollution, health, wildlife mapping, ?sheries and remote sensing, amongst others. This book contains selected contributions from geoENV VII, the 7th Int- national Conference on Geostatistics for Environmental Applications, held in Southampton, UK, in September 2008. Like previous conferences in the series, the meeting attracted a diversity of researchers from across Europe and further a?eld. A total of 82 abstracts were submitted to the conference and from these the organisation committee selected 46 papers for oral presentation and 30 for poster presentation. The chapters contained in the book represent the state-of-the-art in geostatistics for the environmental sciences. The book includes 35 chapters arranged according to their main focus, whether methodological, or in a particular application. All of the chapters included were accepted after review by members of the scienti?c c- mittee and each chapter was also subject to checks by the editors.

Semi-infinite programming (SIP) deals with optimization problems in which either the number of decision variables or the number of constraints is finite. This book presents the state of the art in SIP in a suggestive way, bringing the powerful SIP tools close to the potential users in different scientific and technological fields. The volume is divided into four parts. Part I reviews the first decade of SIP (1962-1972). Part II analyses convex and generalised SIP, conic linear programming, and disjunctive programming. New numerical methods for linear, convex, and continuously differentiable SIP problems are proposed in Part III. Finally, Part IV provides an overview of the applications of SIP to probability, statistics, experimental design, robotics, optimization under uncertainty, production games, and separation problems. Audience: This book is an indispensable reference and source for advanced students and researchers in applied mathematics and engineering.

In 1945, very early in the history of the development of a rigorous analytical theory of probability, Feller (1945) wrote a paper called "The fundamental limit theorems in probability" in which he set out what he considered to be "the two most important limit theorems in the modern theory of probability: the central limit theorem and the recently discovered ... 'Kolmogoroff's cel ebrated law of the iterated logarithm' ." A little later in the article he added to these, via a charming description, the "little brother (of the central limit theo rem), the weak law of large numbers," and also the strong law of large num bers, which he considers as a close relative of the law of the iterated logarithm. Feller might well have added to these also the beautiful and highly applicable results of renewal theory, which at the time he himself together with eminent colleagues were vigorously producing. Feller's introductory remarks include the visionary: "The history of probability shows that our problems must be treated in their greatest generality: only in this way can we hope to discover the most natural tools and to open channels for new progress. This remark leads naturally to that characteristic of our theory which makes it attractive beyond its importance for various applications: a combination of an amazing generality with algebraic precision."

Preservation of Moduli of Continuity for BersteinType Operators (J.A. Adell, J. de la Cal). Lp-Korovkin Type Inequalities for Positive Linear Operators (G.A. Anastassiou). On Some ShiftInvariate Integral Operators, Multivariate Case (G.A. Anastassiou, H.H. Gonska). Multivariate Probabalistic Wavelet Approximation (G. Anastassiou et al.). Probabalistic Approach to the Rounding Problem with Applications to Fair Representation (B. Athanasopoulos). Limit Theorums for Random Multinomial Forms (A. Basalykas). Multivariate Boolean Trapezoidal Rules (G. Baszenski, F.J. Delvos). Convergence Results for an Extension of the Fourier Transform (C. Belingeri, P.E. Ricci). The Action Constants (B.L. Chalmers, B. Shekhtman). Bivariate Probability Distributions Similar to Exponential (B. Dimitrov et al.). Probability, Waiting Time Results for Pattern and Frequency Quotas in the Same Inverse Sampling Problem Via the Dirichlet (M. Ebneshahrashoob, M. Sobel). 25 additional articles. Index.

This volume contains a selection of invited papers, presented to the fourth International Conference on Statistical Data Analysis Based on the L1-Norm and Related Methods, held in Neuchatel, Switzerland, from August 4-9, 2002. The contributions give evidence of the importance of development of theory, methods and applications related to the statistical data analysis based on the L1-norm. Covering a broad range of topics around statistical data analysis, the contents are intended as a resource for researchers, practitioners and industrial statisticians. Several contributions can also be used by financial economists, environmental engineers and professionals in image processing.

Designed to help you overcome your apprehension about statistics, UNDERSTANDING BASIC STATISTICS, ENHANCED, 7E, INTERNATIONAL METRIC EDITION provides plenty of guidance and informal advice as it demonstrates the links between statistics and the real world. The text's reader-friendly approach helps you grasp the concepts and see how they relate to your life. A complete technology package, including JMP (R) statistical software, gives you the tools you need to practice what you're learning and succeed in the course.

Gini's mean difference (GMD) was first introduced by Corrado Gini in 1912 as an alternative measure of variability. GMD and the parameters which are derived from it (such as the Gini coefficient or the concentration ratio) have been in use in the area of income distribution for almost a century. In practice, the use of GMD as a measure of variability is justified whenever the investigator is not ready to impose, without questioning, the convenient world of normality. This makes the GMD of critical importance in the complex research of statisticians, economists, econometricians, and policy makers. This book focuses on imitating analyses that are based on variance by replacing variance with the GMD and its variants. In this way, the text showcases how almost everything that can be done with the variance as a measure of variability, can be replicated by using Gini. Beyond this, there are marked benefits to utilizing Gini as opposed to other methods. One of the advantages of using Gini methodology is that it provides a unified system that enables the user to learn about various aspects of the underlying distribution. It also provides a systematic method and a unified terminology. Using Gini methodology can reduce the risk of imposing assumptions that are not supported by the data on the model. With these benefits in mind the text uses the covariance-based approach, though applications to other approaches are mentioned as well.

This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference "Modern problems of stochastic analysis and statistics", held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.

This book illustrates the current work of leading multilevel modeling (MLM) researchers from around the world.

The book's goal is to critically examine the real problems that occur when trying to use MLMs in applied research, such as power, experimental design, and model violations. This presentation of cutting-edge work and statistical innovations in multilevel modeling includes topics such as growth modeling, repeated measures analysis, nonlinear modeling, outlier detection, and meta analysis.

This volume will be beneficial for researchers with advanced statistical training and extensive experience in applying multilevel models, especially in the areas of education; clinical intervention; social, developmental and health psychology, and other behavioral sciences; or as a supplement for an introductory graduate-level course.

This graduate-level textbook presents an introduction to Bayesian statistics and decision theory. Its scope covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics such as complete class theorems, the Stein effect, Bayesian model choice, hierarchical and empirical Bayes modeling, Monte Carlo integration, including Gibbs sampling and other MCMC techniques. The second edition includes a new chapter on model choice (Chapter 7) and the chapter on Bayesian calculations (6) has been extensively revised. Chapter 4 includes a new section on dynamic models. In Chapter 3, the material on noninformative priors has been expanded, and Chapter 10 has been supplemented with more examples. The Bayesian Choice will be suitable as a text for courses on Bayesian analysis, decision theory or a combination of them. Christian P. Robert is Professor of Statistics in the Applied Mathematics Department at the Université Paris Dauphine, and external lecturer at Ecole Polytechnique, Palaiseau, France. He was previously Head of the Statistics Laboratory at the Center for Research in Economics and Statistics (CREST) of the National Institute for Statistics and Economic Studies (INSEE) in Paris. In addition to many papers on Bayesian statistics, simulation methods, and decision theory, he has written three other books, including Monte Carlo Statistical Method (Springer 1999) with George Casella. He also edited Discretization and MCMC Convergence Assessment (Springer 1998). He has served or is serving as an associate editor for the Annals of Statistics, the Journal of the American Statistical Association, Statistical Science, and Sankhya. He is a fellow of the Institute of Mathematical Statistics, and the Young Statistician Award of the Société de Statistique de Paris in 1995.

One SCI\'ice mathematics bas rendered the 'Et moi, ...si j'avait su comment en revcnir. je n'y serais point aile: human race. It bas put common sc:nsc back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded n- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. :; 'One service logic has rendered com- puter science .. :; 'One service category theory has rendered mathematics .. :. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Spatial point processes play a fundamental role in spatial statistics and today they are a very active area of research with many new and emerging applications. Although published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and nowhere can one find a comprehensive treatment of the theory and applications of simulation-based inference. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo (MCMC) algorithms and explore one of the most important recent developments in MCMC-perfect simulation procedures.

Outstanding User Interfaces with Shiny provides the reader with necessary knowledge to develop beautiful and highly interactive user interfaces. It gives the minimum requirements in HTML/JavaScript and CSS to be able to extend already existing Shiny layouts or develop new templates from scratch. Suitable for anyone with some experience of Shiny, package development and software engineering best practices, this book is an ideal guide for graduates and professionals who wish to bring their app design to the next level. Key Features: Provides a survival kit in web development to seamlessly get started with HTML/CSS/JavaScript Leverage CSS and Sass and higher-level tools like {bslib} to substantially enhance the design of your app in no time A comprehensive guide to the {htmltools} package to seamlessly customize existing layouts Describes in detail how Shiny inputs work and how R and JavaScript communicate Details all the necessary steps to create a production-grade custom template from scratch: packaging, shiny tags creation, validating and testing R components and JavaScript Expose common web development debugging technics Provides a list of existing templates, resources to get started and to explore

LONGLISTED FOR THE CRICKET SOCIETY AND MCC BOOK OF THE YEAR AWARD 2023. "Fascinating" The Observer "Illuminating" The Times "Crickonomics is packed with sufficient statistical analysis to have the most ardent cricket geek purring with pleasure" Mail on Sunday "An insightful, Hawk-Eye-like analysis of the numbers behind cricket" Financial Times An engaging tour of the modern game from an award-winning journalist and the economist who co-authored the bestselling Soccernomics. Why does England rely on private schools for their batters - but not their bowlers? How did demographics shape India's rise? Why have women often been the game's great innovators? Why does South Africa struggle to produce Black Test batters? And how does the weather impact who wins? Crickonomics explores all of this and much more - including how Jayasuriya and Gilchrist transformed Test batting but T20 didn't; English cricket's great missed opportunity to have a league structure like football; why batters are paid more than bowlers; how Afghanistan is transforming German cricket; what the rest of the world can learn from New Zealand and even the Barmy Army's importance to Test cricket. This incisive book will entertain and surprise all cricket lovers. It might even change how you watch the game.

Because of its potential to "predict the unpredictable," Extreme Value Theory (EVT) and its methodology are currently in the spotlight. EVT affords some insight into extreme tails and maxima where standard models have proved unreliable. This is achieved with semi-parametric models which only specify the distributional shapes of maxima or of extreme tails. The rationale for these models are very basic limit and stability arguments.

Bringing together world-recognized authorities, Extreme Values in Finance, Telecommunications, and the Environment puts to rest some of the myths and misconceptions of EVT. It explores the application, use, and theory of extreme values in the areas of finance, insurance, the environment, and telecommunications. The book reviews the way in which this paradigm can answer questions in climatology, insurance, and finance, covers parts of univariate extreme values theory, and discusses estimation, diagnostics, and multivariate extremes. It presents issues in data network modeling and examines aspects of Value-at-Risk (VaR) and its estimation based on EVT. The final chapter gives an overview of multivariate extreme value distributions and the problem of measuring extremal dependencies.

Considered one of the hottest ideas in risk management, EVT is designed to allow anyone faced with calculating risky situations to determine the chances of being hit with one or even multiple catastrophic events. It provides a statistical methodology for dealing with the prediction of events which are so rare that they appear impossible. Presenting information from the forefront of knowledge and research, Extreme Values in Finance, Telecommunications, and the Environment brings you up to speed on current issues and techniques in EVT.

The application of auto-repeat facilities in telephone systems, as well as the use of random access protocols in computer networks, have led to growing interest in retrial queueing models. Since much of the theory of retrial queues is complex from an analytical viewpoint, with this book the authors give a comprehensive and updated text focusing on approximate techniques and algorithmic methods for solving the analytically intractable models.

Retrial Queueing Systems: A Computational Approach also

• Presents motivating examples in telephone and computer networks.
• Establishes a comparative analysis of the retrial queues versus standard queues with waiting lines and queues with losses.
• Integrates a wide range of techniques applied to the main M/G/1 and M/M/c retrial queues, and variants with general retrial times, finite population and the discrete-time case.
• Surveys basic results of the matrix-analytic formalism and emphasizes the related tools employed in retrial queues.
• Discusses a few selected retrial queues with QBD, GI/M/1 and M/G/1 structures.
• Features an abundance of numerical examples, and updates the existing literature.

The book is intended for an audience ranging from advanced undergraduates to researchers interested not only in queueing theory, but also in applied probability, stochastic models of the operations research, and engineering. The prerequisite is a graduate course in stochastic processes, and a positive attitude to the algorithmic probability.

Change-point problems arise in a variety of experimental and mathematical sciences, as well as in engineering and health sciences. This rigorously researched text provides a comprehensive review of recent probabilistic methods for detecting various types of possible changes in the distribution of chronologically ordered observations. Further developing the already well-established theory of weighted approximations and weak convergence, the authors provide a thorough survey of parametric and non-parametric methods, regression and time series models together with sequential methods. All but the most basic models are carefully developed with detailed proofs, and illustrated by using a number of data sets. Contains a thorough survey of:

• The Likelihood Approach
• Non-Parametric Methods
• Linear Models
• Dependent Observations