Sandsynlighedsregning og statistik

The Encyclopedia of Mathematical Geosciences is a complete and authoritative reference work. It provides concise explanation on each term that is related to Mathematical Geosciences. Over 300 international scientists, each expert in their specialties, have written around 350 separate articles on different topics of mathematical geosciences including contributions on Artificial Intelligence, Big Data, Compositional Data Analysis, Geomathematics, Geostatistics, Geographical Information Science, Mathematical Morphology, Mathematical Petrology, Multifractals, Multiple Point Statistics, Spatial Data Science, Spatial Statistics, and Stochastic Process Modeling. Each topic incorporates cross-referencing to related articles, and also has its own reference list to lead the reader to essential articles within the published literature. The entries are arranged alphabetically, for easy access, and the subject and author indices are comprehensive and extensive.

This book introduces the Learning-Augmented Network Optimization (LANO) paradigm, which interconnects network optimization with the emerging AI theory and algorithms and has been receiving a growing attention in network research. The authors present the topic based on a general stochastic network optimization model, and review several important theoretical tools that are widely adopted in network research, including convex optimization, the drift method, and mean-field analysis. The book then covers several popular learning-based methods, i.e., learning-augmented drift, multi-armed bandit and reinforcement learning, along with applications in networks where the techniques have been successfully applied. The authors also provide a discussion on potential future directions and challenges.

Einsendeaufgabe aus dem Jahr 2023 im Fachbereich Mathematik - Statistik, Note: 1,7, SRH Fernhochschule, Sprache: Deutsch, Abstract: Diese Einsendeaufgabe beschäftigt sich mit der quantitativen Datenanalyse. Aufgabe 1 behandelt Grundlagen und Arten der Varianzanalyse (ANOVA), z.B. die mehrfaktorielle Varianzanalyse. Aufgabe 2 befasst sich mit dem Levene-Test und T-Test, speziell mit der Durchführung und Interpretation mit der Software SPSS. Aufgabe 3 beschäftigt sich mit der deskriptiven, inferenzstatistischen und Regressionsanalyse. Außerdem werden das Verfahren der Pearson-Korrelation, die Spearman-Korrelation und der Kolmogorov-Smirnov-Test angewendet.

This book provides the essential theoretical tools for stochastic modeling. The authors address the most used models in applications such as Markov chains with discrete-time parameters, hidden Markov chains, Poisson processes, and birth and death processes. This book also presents specific examples with simulation methods that apply the topics to different areas of knowledge. These examples include practical applications, such as modeling the COVID-19 pandemic and animal movement modeling. This book is concise and rigorous, presenting the material in an easily accessible manner that allows readers to learn how to address and solve problems of a stochastic nature.

This innovative textbook presents material for a course on industrial statistics that incorporates Python as a pedagogical and practical resource. Drawing on many years of teaching and conducting research in various applied and industrial settings, the authors have carefully tailored the text to provide an ideal balance of theory and practical applications. Numerous examples and case studies are incorporated throughout, and comprehensive Python applications are illustrated in detail. A custom Python package is available for download, allowing students to reproduce these examples and explore others.The first chapters of the text focus on the basic tools and principles of process control, methods of statistical process control (SPC), and multivariate SPC. Next, the authors explore the design and analysis of experiments, quality control and the Quality by Design approach, computer experiments, and cyber manufacturing and digital twins. The text then goes on to cover reliability analysis, accelerated life testing, and Bayesian reliability estimation and prediction. A final chapter considers sampling techniques and measures of inspection effectiveness. Each chapter includes exercises, data sets, and applications to supplement learning.Industrial Statistics: A Computer-Based Approach with Python is intended for a one- or two-semester advanced undergraduate or graduate course. In addition, it can be used in focused workshops combining theory, applications, and Python implementations. Researchers, practitioners, and data scientists will also find it to be a useful resource with the numerous applications and case studies that are included.A second, closely related textbook is titled Modern Statistics: A Computer-Based Approach with Python. It covers topics such as probability models and distribution functions, statistical inference and bootstrapping, time series analysis and predictions,and supervised and unsupervised learning. These texts can be used independently or for consecutive courses.The mistat Python package can be accessed at https://gedeck.github.io/mistat-code-solutions/IndustrialStatistics/."This book is part of an impressive and extensive write up enterprise (roughly 1,000 pages!) which led to two books published by Birkhäuser. This book is on Industrial Statistics, an area in which the authors are recognized as major experts. The book combines classical methods (never to be forgotten!) and "hot topics" like cyber manufacturing, digital twins, A/B testing and Bayesian reliability. It is written in a very accessible style, focusing not only on HOW the methods are used, but also on WHY. In particular, the use of Python, throughout the book is highly appreciated. Python is probably the most important programming language used in modern analytics. The authors are warmly thanked for providing such a state-of-the-art book. It provides a comprehensive illustration of methods and examples based on the authors longstanding experience, and accessible code for learning and reusing in classrooms and on-site applications."Professor Fabrizio RuggeriResearch Director at the National Research Council, ItalyPresident of the International Society for Business and Industrial Statistics (ISBIS)Editor-in-Chief of Applied Stochastic Models in Business and Industry (ASMBI)

Focusing on comprehensive comparisons of the performance of stochastic optimization algorithms, this book provides an overview of the current approaches used to analyze algorithm performance in a range of common scenarios, while also addressing issues that are often overlooked. In turn, it shows how these issues can be easily avoided by applying the principles that have produced Deep Statistical Comparison and its variants. The focus is on statistical analyses performed using single-objective and multi-objective optimization data. At the end of the book, examples from a recently developed web-service-based e-learning tool (DSCTool) are presented. The tool provides users with all the functionalities needed to make robust statistical comparison analyses in various statistical scenarios.The book is intended for newcomers to the field and experienced researchers alike. For newcomers, it covers the basics of optimization and statistical analysis, familiarizing them with the subject matter before introducing the Deep Statistical Comparison approach. Experienced researchers can quickly move on to the content on new statistical approaches. The book is divided into three parts:Part I: Introduction to optimization, benchmarking, and statistical analysis - Chapters 2-4.Part II: Deep Statistical Comparison of meta-heuristic stochastic optimization algorithms - Chapters 5-7.Part III: Implementation and application of Deep Statistical Comparison - Chapter 8.

This SpringerBrief describes the development and use of a synthetic indicator to assess different degrees of sustainability adoption by economic sector and businesses size. To make this analysis a theoretical framework which involves variables common to alternative frameworks (specifically ESG, GRI and Istat) is proposed. The empirical analysis focuses on the environmental, social and economic variables of the Italian businesses. In this analysis, all three pillars of sustainability ¿ economic, environmental, and social ¿ are considered. The work begins with a review of business sustainability literature and a look into institutional frameworks for the development and measurement of the phenomena. Connections between businesses and the SDGs are examined and comparison of the classifications of sustainable activities defined by GRI and ESG international standards is used to define a framework to be adopted to analyse ISTAT Business Census. Selected indicator variables are aggregated with a synthetic indicator and the results are presented (this is a new proposal of a synthetic indicator useful for the type of data used and published by ISTAT ¿ Italian National Statistical Institute), discussing pros and cons of using it. This study provides two important innovative contributions. The first one is about how to approach the theoretical framework of businesses sustainability at firms aggregated level. The basic idea to work on a set of variables common to different approaches is interesting from the interpretative point of view. The second one, is about the specific empirical analysis, i.e. the Italian businesses sustainability situation. The investigation based on this new theoretical classification/framework and the new proposed indicator provides some interesting substantive results.

In commemoration of the bicentennial of the birth of the "e;lady who gave the rose diagram to us"e;, this special contributed book pays a statistical tribute to Florence Nightingale. This book presents recent phenomenal developments, both in rigorous theory as well as in emerging methods, for applications in directional statistics, in 25 chapters with contributions from 65 renowned researchers from 25 countries. With the advent of modern techniques in statistical paradigms and statistical machine learning, directional statistics has become an indispensable tool. Ranging from data on circles to that on the spheres, tori and cylinders, this book includes solutions to problems on exploratory data analysis, probability distributions on manifolds, maximum entropy, directional regression analysis, spatio-directional time series, optimal inference, simulation, statistical machine learning with big data, and more, with their innovative applications to emerging real-life problems in astro-statistics, bioinformatics, crystallography, optimal transport, statistical process control, and so on.

This book provides an overview of Data Monitoring Committees(DMC) - what was done in the past, what is currently being done, and thoughts on improvements for the future. Previous works focused primarily on large cardiovascular studies (where DMCs originated more than 30 years ago) but updated references are needed that discuss smaller, more flexible studies in areas such as oncology. The authors have attended ~800 DMC meetings from ~200 distinct studies across all areas of clinical studies (oncology, rheumatology, rare diseases, cardiology, immunology, etc.) This wide range of expertise will be used, as well as the expertise that comes from working with virtually every large biotechnology and pharmaceutical company and CRO for DMC work. The reader of the book will know when DMCs are needed or helpful, how to form the DMC, how to work with external CROs and with sponsor teams and the DMC to create needed DMC outputs, how the DMC meetings are conducted, and - especially for DMC members - what are considerations within the Closed Session to review safety/efficacy outputs to assess risk/benefit to make appropriate recommendations that protect the patient safety and trial integrity.This is a practical hands-on book on how to decide if a DMC is necessary, how to form the DMC, how to expertly create the necessary materials for the DMC and have smooth running DMC meetings. There is no specialized training in school about how DMCs work - frequently people may have been in industry for many years without ever needing to work with a DMC. This book is the helpful reference for those new to these DMCs. The DMC work is critical to be correctly implemented as the impact of DMC activity on safeguarding the trial is so important.This book provides the following:Provides thorough instructions on the steps needed to form and implement a Data Monitoring Committee for clinical trial evaluation;Includes practical and hands-on information on DMC implementation;Discusses a wide range of clinical trial ¿ by phase and therapeutic area.

This volume collects selected papers from the Ninth High Dimensional Probability Conference, held virtually from June 15-19, 2020. These papers cover a wide range of topics and demonstrate how high-dimensional probability remains an active area of research with applications across many mathematical disciplines. Chapters are organized around four general topics: inequalities and convexity; limit theorems; stochastic processes; and high-dimensional statistics. High Dimensional Probability IX will be a valuable resource for researchers in this area.

This edited volume on machine learning and big data analytics (Proceedings of ICMLBDA 2022) is intended to be used as a reference book for researchers and professionals to share their research and reports of new technologies and applications in Machine Learning and Big Data Analytics like biometric Recognition Systems, medical diagnosis, industries, telecommunications, AI Petri Nets Model-Based Diagnosis, gaming, stock trading, Intelligent Aerospace Systems, robot control, law, remote sensing and scientific discovery agents and multiagent systems; and natural language and Web intelligence.The intent of this book is to provide awareness of algorithms used for machine learning and big data in the advanced Scientific Technologies, provide a correlation of multidisciplinary areas and become a point of great interest for Data Scientists, systems architects, developers, new researchers and graduate level students. This volume provides cutting-edge research from around the globeon this field. Current status, trends, future directions, opportunities, etc. are discussed, making it friendly for beginners and young researchers.

Für empirische Wirtschaftswissenschaftler gehören ökonometrische Methoden zum Standardwerkzeug. Die neuen Instrumente des maschinellen Lernens setzen sich langsam auch in der Volks- und Betriebswirtschaftslehre durch. Das Buch vermittelt Basiswissen zu den spezifischen Methoden des überwachten und unüberwachten Lernens sowie des Verstärkungslernens. Dabei werden die wesentlichen Unterschiede in Bezug auf Ziele, Methoden und Rahmenbedingungen zwischen den Methoden der Ökonometrie und des maschinellen Lernens dargestellt und erörtert.

This book discusses Artificial Neural Networks (ANN) and their ability to predict outcomes using deep and shallow learning principles. The author first describes ANN implementation, consisting of at least three layers that must be established together with cells, one of which is input, the other is output, and the third is a hidden (intermediate) layer. For this, the author states, it is necessary to develop an architecture that will not model mathematical rules but only the action and response variables that control the event and the reactions that may occur within it. The book explains the reasons and necessity of each ANN model, considering the similarity to the previous methods and the philosophical - logical rules.

This book provides quantitative and applied methodologies in the Covid-19 era exploring important issues in demography, population studies, and health. It provides insight into health and health measures as to the healthy life years lost and the healthy life expectancy related to Covid-19 pandemic. It also describes mortality and survival and focuses on data analysis in demography and population studies. Special methods and applications in demography and society are also described, thereby including applications in society, pension and insurance. As such, this book is a valuable guide for researchers, theoreticians and practitioners from various scientific fields.

Probability and Statistics for Physical Sciences, Second Edition is an accessible guide to commonly used concepts and methods in statistical analysis used in the physical sciences. This brief yet systematic introduction explains the origin of key techniques, providing mathematical background and useful formulas. The text does not assume any background in statistics and is appropriate for a wide-variety of readers, from first-year undergraduate students to working scientists across many disciplines.

Suitable for a first undergraduate course in applied probability, this book introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research.

Applied Statistical Modelling for Ecologists provides a gentle introduction to the essential models of applied statistics: linear models, generalized linear models, mixed and hierarchical models. All models are fit with both a likelihood and a Bayesian approach, using several powerful software packages widely used in research publications: JAGS, NIMBLE, Stan, and TMB. In addition, the foundational method of maximum likelihood is explained in a manner that ecologists can really understand. This book is the successor of the widely used Introduction to WinBUGS for Ecologists (Kéry, Academic Press, 2010). Like its parent, it is extremely effective for both classroom use and self-study, allowing students and researchers alike to quickly learn, understand, and carry out a very wide range of statistical modelling tasks. The examples in Applied Statistical Modelling for Ecologists come from ecology and the environmental sciences, but the underlying statistical models are very widely used by scientists across many disciplines. This book will be useful for anybody who needs to learn and quickly become proficient in statistical modelling, with either a likelihood or a Bayesian focus, and in the model-fitting engines covered, including the three latest packages NIMBLE, Stan, and TMB.

This book provides a quick but insightful introduction to Bayesian tracking and particle filtering for a person who has some background in probability and statistics and wishes to learn the basics of single-target tracking. It also introduces the reader to multiple target tracking by presenting useful approximate methods that are easy to implement compared to full-blown multiple target trackers.The book presents the basic concepts of Bayesian inference and demonstrates the power of the Bayesian method through numerous applications of particle filters to tracking and smoothing problems. It emphasizes target motion models that incorporate knowledge about the target¿s behavior in a natural fashion rather than assumptions made for mathematical convenience.The background provided by this book allows a person to quickly become a productive member of a project team using Bayesian filtering and to develop new methods and techniques for problems the team may face.

An important novel menu for Survival Analysis entitled Accelerated Failure Time (AFT) models has been published by IBM (international Businesss Machines) in its SPSS statistical software update of 2023. Unlike the traditional Cox regressions that work with hazards, which are the ratio of deaths and non-deaths in a sample, it works with risk of death, which is the proportion of deaths in the same sample. The latter approach may provide better sensitivity of testing, but has been seldom applied, because with computers risks are tricky and hazards because they are odds are fine. This was underscored in 1997 by Keiding and colleague statisticians from Copenhagen University who showed better-sensitive goodness of fit and null-hypothesis tests with AFT than with Cox survival tests.So far, a controlled study of a representative sample of clinical Kaplan Meier assessments, where the sensitivity of Cox regression is systematically tested against that of AFT modeling, hasnot been accomplished. This edition is the first textbook and tutorial of AFT modeling both for medical and healthcare students and for professionals. Each chapter can be studied as a standalone, and, using, real as well as hypothesized data, it tests the performance of the novel methodology against traditional Cox regressions. Step by step analyses of over 20 data files stored at Supplementary Files at Springer Interlink are included for self-assessment.We should add that the authors are well qualified in their field. Professor Zwinderman is past-president of the International Society of Biostatistics (2012-2015) and Professor Cleophas is past-president of the American College of Angiology (2000-2002). From their expertise they should be able to make adequate selections of modern data analysis methods for the benefit of physicians, students, and investigators. The authors have been working and publishing together for 25 years and their research can be characterized asa continued effort to demonstrate that clinical data analysis is not mathematics but rather a discipline at the interface of biology and mathematics.

This volume draws upon one of the first comprehensive studies on the regional variations of services for aging persons in China to provide an empirical and theoretical understanding of the impact of China's rapidly growing aging population on the country's socioeconomic, cultural, and political systems. In three parts, the manuscript combines case-oriented comparative methods with variable-oriented statistical and GIS analyses to examine the spatial patterns and relationships between supply and demand of affordable and accessible services for aging persons in China. Part one gives a historical review of population aging in China, including the development of services for aging persons and government policies and programs geared towards elders. Part two provides an analysis of spatial variations of supply and demand for services including food, housing, health, and community services for aging persons. Part three uses case studies to analyse the regional and local dimensions of elderly services.  Suggestions are made for future planning, development, and policies. This book will appeal to policy makers, city planners, service providing businesses, and advanced undergraduate and graduate students studying economic geography, planning, and regional development.

This book focuses on recent advances, approaches, theories, and applications related Hidden Markov Models (HMMs). In particular, the book presents recent inference frameworks and applications that consider HMMs. The authors discuss challenging problems that exist when considering HMMs for a specific task or application, such as estimation or selection, etc. The goal of this volume is to summarize the recent advances and modern approaches related to these problems. The book also reports advances on classic but difficult problems in HMMs such as inference and feature selection and describes real-world applications of HMMs from several domains. The book pertains to researchers and graduate students, who will gain a clear view of recent developments related to HMMs and their applications.

This book provides an overview of the role of statistics in Risk Analysis, by addressing theory, methodology and applications covering the broad scope of risk assessment in life sciences and public health, environmental science as well as in economics and finance. Experimental Design plays a key role in many of these areas, therefore there is special attention paid to joining Risk Analysis and Experimental Design topics. The contributions of this volume originate from the 8th International Conference on Risk Analysis (23-26 April, 2019, Vienna). The conference brought together researchers and practitioners working in the field of Risk Analysis. The most important contributions at the conference have been refereed and developed into chapters to show the latest developments in the field.

This volume presents the revised papers of the 14th International Conference in Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2020, which took place online during August 10-14, 2020. This book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in statistics, machine learning, finance, and computer graphics, offering information on the latest developments in Monte Carlo and quasi-Monte Carlo methods and their randomized versions.