Sandsynlighedsregning og statistik

This book provides readers with a brief account of the history of Language Identification (LI) research and a survey of the features and methods most used in LI literature. LI is the problem of determining the language in which a document is written and is a crucial part of many text processing pipelines. The authors use a unified notation to clarify the relationships between common LI methods. The book introduces LI performance evaluation methods and takes a detailed look at LI-related shared tasks. The authors identify open issues and discuss the applications of LI and related tasks and proposes future directions for research in LI.

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The expansion and constant complication of the scope of research objects requires the development of new effective methods and algorithms for adaptive identification, state assessment and management in uncertainty conditions based on the concept of conditional Gaussian filtering. Also, in the non-parametric description of correlation interactions requires the development of systematic algorithms for conditional-optimal filtering of control objects and adaptive assessment of the state of control objects, taking into account parametric upheavals. In addition, it would be expedient to develop stable algorithms for suboptimal assessment of the state of control objects, extended state vectors of controlled objects, as well as stable algorithms for multi-step assessment of the state of nonlinear control objects. The monograph considers the development of algorithms and computational schemes for adaptive assessment of the state of stochastic control objects on the basis of the conditional Gaussian filtering method and methods of their practical application.

The Monte Carlo methods are widely used in many fields of modern science and technology. As an effective tool for multivariate statistical analysis, the statistical depth function has been used to extend the order statistics in multivariate statistical analysis. It has high robustness and has attracted more and more people's attention. This book mainly studies the approximate computation of statistical depth function based on Monte Carlo methods and its extension in regression analysis.

This book presents an up-to-date perspective on randomized response techniques (RRT). It discusses the most appropriate and efficient procedures of RRT for analysing data from queries dealing with sensitive and confidential issues, including the treatment of infinite and finite population setups. The book aims to spark a renewed interest among sampling experts who may have overlooked RRT. By addressing the missing topics and incorporating a wide range of contributors' works, it seeks to foster an appreciative academic environment and inspire a reformed and amended view of RRT. As the book unfolds, readers will gain valuable insights into the evolving landscape of RRT and its applications, positioning them at the forefront of this engaging field of study.On RRT, the literature has grown immensely since its inception in 1965 by S.L. Warner. Despite several books published on the subject, there are still two crucial topics missing from the existing RRT literature. This book aimsto address these gaps and provide valuable insights to curious readers in the field. The book is mandatory reading for statisticians and biostatisticians, market researchers, operations researchers, pollsters, sociologists, political scientists, economists and advanced undergraduate and graduate students in these areas.

This book provides a systematic presentation of the major results in the field of the theory of k-out-of-n systems obtained in recent years and their applications for the reliability assessment of high-altitude unmanned platforms. Mathematical models, methods, and algorithms, presented in the book, will make a significant contribution to the development of reliability theory and the theoretical foundations of unmanned UAV-based aerial communications networks in the framework of the concept of creating the 5G and beyond networks. The book gives a description of new mathematical methods and approaches (based on decomposable semi-regenerative processes, simulation and machine learning methods, and inventory models) to the study of the complex k-out-of-n systems, which makes it possible to carry out numerical calculations of reliability indicators. Organized into five chapters, each chapter begins with a summary of the main definitions andresults contained in the chapter. The content of this book is based on the original results developed by the authors, many of which appear for the first time in book form.

Large numbers of studies of the KdV equation have appeared since the pioneering paper by Gardner, Greene, Kruskal, and Miura in 1967. Most of those works have employed the inverse spectral method for 1D Schrödinger operators or an advanced Fourier analysis. Although algebraic approaches have been discovered by HirotäSato and Marchenko independently, those have not been fully investigated and analyzed. The present book offers a new approach to the study of the KdV equation, which treats decaying initial data and oscillating data in a unified manner. The author¿s method is to represent the tau functions introduced by HirotäSato and developed by Segal¿Wilson later in terms of the Weyl¿Titchmarsh functions (WT functions, in short) for the underlying Schrödinger operators. The main result is stated by a class of WT functions satisfying some of the asymptotic behavior along a curve approaching the spectrum of the Schrödinger operators at +¿ in an order of -(n-1/2)for the nth KdV equation. This class contains many oscillating potentials (initial data) as well as decaying ones. Especially bounded smooth ergodic potentials are included, and under certain conditions on the potentials, the associated Schrödinger operators have dense point spectrum. This provides a mathematical foundation for the study of the soliton turbulence problem initiated by Zakharov, which was the author¿s motivation for extending the class of initial data in this book. A large class of almost periodic potentials is also included in these ergodic potentials. P. Deift has conjectured that any solutions to the KdV equation starting from nearly periodic initial data are almost periodic in time. Therefore, our result yields a foundation for this conjecture. For the reader¿s benefit, the author has included here (1) a basic knowledge of direct and inverse spectral problem for 1D Schrödinger operators, including the notion of the WT functions; (2)Satös Grassmann manifold method revised by Segal¿Wilson; and (3) basic results of ergodic Schrödinger operators.

Elevate your machine learning skills using the Conformal Prediction framework for uncertainty quantification. Dive into unique strategies, overcome real-world challenges, and become confident and precise with forecasting.Key Features:Master Conformal Prediction, a fast-growing ML framework, with Python applicationsExplore cutting-edge methods to measure and manage uncertainty in industry applicationsUnderstand how Conformal Prediction differs from traditional machine learningBook Description:In the rapidly evolving landscape of machine learning, the ability to accurately quantify uncertainty is pivotal. The book addresses this need by offering an in-depth exploration of Conformal Prediction, a cutting-edge framework to manage uncertainty in various ML applications.Learn how Conformal Prediction excels in calibrating classification models, produces well-calibrated prediction intervals for regression, and resolves challenges in time series forecasting and imbalanced data. Discover specialised applications of conformal prediction in cutting-edge domains like computer vision and NLP. Each chapter delves into specific aspects, offering hands-on insights and best practices for enhancing prediction reliability. The book concludes with a focus on multi-class classification nuances, providing expert-level proficiency to seamlessly integrate Conformal Prediction into diverse industries. With practical examples in Python using real-world datasets, expert insights, and open-source library applications, you will gain a solid understanding of this modern framework for uncertainty quantification.By the end of this book, you will be able to master Conformal Prediction in Python with a blend of theory and practical application, enabling you to confidently apply this powerful framework to quantify uncertainty in diverse fields.What You Will Learn:The fundamental concepts and principles of conformal predictionLearn how conformal prediction differs from traditional ML methodsApply real-world examples to your own industry applicationsExplore advanced topics - imbalanced data and multi-class CPDive into the details of the conformal prediction frameworkBoost your career as a data scientist, ML engineer, or researcherLearn to apply conformal prediction to forecasting and NLPWho this book is for:Ideal for readers with a basic understanding of machine learning concepts and Python programming, this book caters to data scientists, ML engineers, academics, and anyone keen on advancing their skills in uncertainty quantification in ML.

Taking an amusing and digestible look at the usually dry world of probability and statistics, this is the ultimate guide to how you can incorporate them into everyday life, from one of the world's most sought-after experts in game theory.This book reveals how statistics and probability are fundamental to our everyday life – from advertisements to public-opinion polls, weather forecasts to government policies, scientific research to stock market information. Haim Shapira then presents a myriad of anecdotes, riddles, case studies and practical exercises in his trademark witty voice to guide the reader through the importance of statistics and probability in everyday life. Some examples include:making sense of NBA stats – discover who is the greatest scorer of all timea beginner's guide to gambling successfullywhy events of very low probability have happened, are happening and will happenwhat role stats has to play in flat-earth conspiracy argumentsthe likelihood of winning the lotterymisconceptions about statistical findings surrounding COVID-19what "beyond reasonable doubt" really meansa case of misunderstood probabilities in the Sally Clarke and OJ Simpson trialsWith easy-to-follow explanations, tables and graphs of all the maths behind the statistics – averages, standard deviation, percentiles, logarithmic scales, correlation coefficient – this book provides everything you need to know to determine your options and calculate your chance of success, thereby learning to make better decisions.

"Tales of the Tail: Legendary Cats Throughout History" is an enchanting exploration into the feline realm, delving into the captivating stories of extraordinary cats that have left an indelible mark on human history. This whimsical tome unveils the rich tapestry of legends, folklore, and real-life anecdotes surrounding these enigmatic creatures, celebrating their mystique and the profound impact they have had on various cultures.Within the pages of "Tales of the Tail," readers will embark on a journey through time, discovering mythical cats that have been revered as divine entities, guardians, and symbols of good fortune. From ancient civilizations to modern times, the book weaves together narratives of cats that have transcended the ordinary, earning their place as revered beings in the annals of history.The tales within this collection are not limited to mere whimsy; they are intertwined with historical events, cultural beliefs, and the evolving roles that cats have played in societies around the world. Whether exploring the sacred cats of ancient Egypt, the mischievous Cheshire Cat of Wonderland fame, or the famed literary cat companions of renowned authors, each story is a testament to the profound connections between humans and their feline counterparts.Each chapter unfolds like a storybook, with vivid descriptions and captivating illustrations bringing these legendary cats to life. From the graceful and regal to the cunning and magical, "Tales of the Tail" pays homage to the diverse personalities and qualities that have made cats such beloved companions throughout the ages.This enchanting collection is a celebration of the enduring fascination with cats and their timeless allure. "Tales of the Tail" invites readers to immerse themselves in the magical world of legendary felines, where history, mythology, and the timeless charm of cats converge in a purrfectly delightful tapestry of tales.

This book provides solid sociological foundations to computational social science (CSS). CSS is an emerging research field, and many books with those words in the title are on the market. However, CSS has not become mainstream in sociology, for which there are two reasons. First, CSS does not necessarily solve major research questions in sociology. Second, its sociological foundations are weak. These two reasons are interrelated¿that is, CSS cannot solve major research questions because its sociological foundations are weak. Thus, even if it tries to solve those questions, its approaches seem to mainstream sociologists to miss the point. To resolve that shortcoming, this book fills the gap between CSS and sociology, shows that CSS can solve major research questions in sociology, and advances sociology by introducing to it theories and methodologies of CSS.

This textbook invites readers to explore mathematical thinking by finding the beauty in the subject. With an accessible tone and stimulating puzzles, the author will convince curious non-mathematicians to continue their studies in the area. It has an expansive scope, covering everything from probability and graph theory to infinities and Newton¿s method. Many examples of proofs appear as well, offering readers the opportunity to explore these topics with the amount of rigor that suits them. Programming exercises in Python are also included to show how math behaves in action.Mathematical Thinking is an ideal textbook for transition courses aimed at undergraduates moving from lower level to more advanced topics, as well as for math recruitment and invitational courses at the freshman or sophomore level. It may also be of interest in computer science departments and can be used as a supplemental text for courses in discrete mathematics and graph theory.

Comparing the clusters obtained by two statistical grouping techniques, hierarchical and k-means, we examine the results of the 2013 Saber 11 tests in Bogotá schools, contrasting the factors: sector, calendar and school day, to characterize the schools, forming three groups: high, medium and low averages, according to the average score obtained by institution in the areas of the common core. The results reveal, although there are discrepancies in the clusters formed between techniques in terms of the number of schools per group and centroid values, that the differences according to: nature, sector and timetable are marked. In general, in both techniques: group 1 is almost entirely made up of non-official schools, with less than 1.18% of official schools and more than 77.51% have a full day. The majority of official schools are in group 3, with more than 57.56%. More than 88.46% of the B calendar schools belong to group 1. The F calendar schools are located; more than 83.38% in group 3 and less than 7.65% in group 1. While 100% of Saturday schools, more than 92.61% of evening schools and more than 61.24% of afternoon schools belong to group 3.

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space¿a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees.While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

This book deals with the first discriminant theory of linearly separable data (LSD), Theory3, based on the four ordinary LSD of Theory1 and 169 microarrays (LSD) of Theory2. Furthermore, you can quickly analyze the medical data with the misclassified patients which is the true purpose of diagnoses. Author developed RIP (Optimal-linear discriminant function finding the combinatorial optimal solution) as Theory1 in decades ago, that found the minimum misclassifications. RIP discriminated 63 (=26¿1) models of Swiss banknote (200*6) and found the minimum LSD: basic gene set (BGS). In Theory2, RIP discriminated Shipp microarray (77*7129) which was LSD and had only 32 nonzero coefficients (first Small Matryoshka; SM1). Because RIP discriminated another 7,097 genes and found SM2, the author developed the Matryoshka feature selection Method 2 (Program 3), that splits microarray into many SMs. Program4 can split microarray into many BGSs. Then, the wide columnLSD (Revolution-0), such as microarray (n5) models, including BGS, become LSD among (219¿1) models. Because Program2 confirms BGS has the minimum average error rate, BGS is the most compact and best model satisfying Occam¿s Razor. With this book, physicians obtain complete diagnostic results for disease, and engineers can become a true data scientist, by obtaining integral knowledge ofstatistics and mathematical programming with simple programs.

This revised book provides an accessible presentation of concepts from probability theory, statistical methods, the design of experiments, and statistical quality control. It is shaped by the experience of the two teachers teaching statistical methods and concepts to engineering students. Practical examples and end-of-chapter exercises are the highlights of the text, as they are purposely selected from different fields. Statistical principles discussed in the book have a great relevance in several disciplines like economics, commerce, engineering, medicine, health care, agriculture, biochemistry, and textiles to mention a few.Organised into 16 chapters, the revised book discusses four major topics¿probability theory, statistical methods, the design of experiments, and statistical quality control. A large number of students with varied disciplinary backgrounds need a course in basics of statistics, the design of experiments and statistical quality control at an introductory level to pursue their discipline of interest. No previous knowledge of probability or statistics is assumed, but an understanding of calculus is a prerequisite. The whole book also serves as a master level introductory course in all the three topics, as required in textile engineering or industrial engineering.

This book compares the population history of Japan, Korea, Taiwan, and China to understand such emergent changes as extremely low fertility in Korea and Taiwan, compressed urbanization and a massive diaspora from Korea, early population aging relative to economic development in China, and changing patterns of cross-border migration in the region. After discussing the origin of each ethnic group, premodern population changes are examined by reviewing historical demographic studies including those written in local languages. A new population estimation for premodern Korea is also presented. Topics covered in this book include population growth, fertility, mortality, domestic and cross-border migration, marriage, divorce, and households. Contrasts between economic and population giants (China and Japan), former Japanese colonies (Korea and Taiwan), feudalism and Confucianism (Japan and others), and capitalism and socialism of the same ethnic groups (South and North Korea, Taiwan, and China) provide a fresh view of population dynamics in relation to political, economic, and cultural changes. The population study of Eastern Asia has great importance. If economic development is checked by early and rapid aging, it functions to preserve the conventional Euro-centric world system and Pax Americana. On the other hand, if China succeeds in further development while sustaining a socialist dictatorship, it is a challenge to the authority of liberal democracy. If the institution of marriage remains robust and extramarital births do not increase in Eastern Asia, it implies that an aspect of family change is culturally dependent. This book provides clues to help answer such important questions.