Finite Difference Computing with Exponential Decay Models
Throughout industry and science it is common today to study nature or technological devices through models on a computer. With such models the computer acts as a virtual lab where experiments can be done in a fast, reliable, safe, and cheap way. In some fields, e.g., aerospace engineering, the computer models are now so sophisticated that they can replace physical experiments to a large extent
This book starts by presenting an overview of the statistical thought process. By the end of chapter 2, students are already familiar with concepts such as hypotheses, level of significance, p-values, errors. Normally these topics are not introduced until after a discussion of probability and sampling distributions. My approach to probability and sampling distributions is also very different. Because students using this book know about hypotheses before we reach the probability section, inferential theory can be developed by applying the probability rules the testing of a hypothesis. To me, this leads to better and more interesting questions than are typically asked in these sections and gives meaning to these concepts. Other differences include homework problems that require the integration of topics from different chapters as well as one problem in each chapter based on issues discussed in other classes on our campus (e.g. psychology, criminal justice, economics, etc).
This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons which underlie the rules of probability are emphasized. Probability theory is certainly useful. But how does it feel to study it? Well, like other areas of mathematics, probability theory contains elegant concepts, and it gives you a chance to exercise your ingenuity, which is often fun. But in addition, randomness and probability are part of our experience in the real world, present everywhere and yet still somewhat mysterious.
The target audience for this book is college students who are required to learn statistics, students with little background in mathematics and often no motivation to learn more. It is assumed that the students do have basic skills in using computers and have access to one. Moreover, it is assumed that the students are willing to actively follow the discussion in the text, to practice, and more importantly, to think.
This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.
The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. The inaugural effort is OpenIntro Statistics. Probability is optional, inference is key, and we feature real data whenever possible. License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remiThe OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. The inaugural effort is OpenIntro Statistics. Probability is optional, inference is key, and we feature real data whenever possible. License: Creative Commons Attribution Sharealike. This license is considered to be some to be the most open license. It allows reuse, remixing, and distribution (including commercial), but requires any remixes use the same license as the original. This limits where the content can be remixed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.xed into, but on the other hand ensures that no-one can remix the content then put the remix under a more restrictive license.
The concepts and basic topics in elementary Linear Algebra and Calculus are reviewed and generalized to Linear Analysis in this first unit. In particular, the dot product, the vector space of R 2(that is, the x − y plane in Plane Geometry), and measurement of lengths of vectors in R2 , are extended to the “inner product,” the “inner-product space,” and “norm” measurement, respectively; the notion of eigenvalues and eigenvectors from Linear Algebra is extended to the “eigenvalue problem” of bounded linear operators; and eigenvalues are replaced by singular values for self-adjoint positive definite linear operators.
https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2014/11/MA304- TopicsInAppliedMathematics-FINAL.pdf
Learning Statistics with jamovi: A Tutorial for Beginners in Statistical Analysis
Based on Danielle Navarro’s widely acclaimed and prize-winning book Learning Statistics with R, this elegantly designed textbook offers undergraduate students a thorough and accessible introduction to jamovi, as well as how to get to grips with statistics and data manipulation.
Wearable Electronics and Embedded Computing Systems
The application of wearable electronics in the biomedical research and commercial fields has been gaining great interest over the last several decades. Small-sized, lightweight monitoring systems with low-power consumption and, of course, wearability allow for the collection of physiological and behavioral data in ecological scenarios (e.g., at home, during daily activities or sleep, during specific tasks, etc.) with a minimal discomfort for the end user [1]. As a result, outpatient-monitoring care can be associated with improved quality of life, especially for patients with chronic disease, possibly preventing unnecessary hospitalizations and reducing direct and indirect healthcare costs.
Enzo Pasquale Scilingo -, Gaetano Valenza
MDPI - Multidisciplinary Digital Publishing Institute
Optimal scheduling is an important area of operations research, as it has both theoretical and practical aspects. It is clear that efficient algorithms are most desirable for practical applications, since most real-world scheduling problems have large sizes but require fast decisions. Due to this, practitioners often prefer to use rather simple algorithms which provide schedules that may be far from optimal with respect to their quality. This book is based on a Special Issue entitled ”Algorithms for Scheduling Problems”. In the Call for Papers, we invited prospective authors to submit their latest research in the area of the development of scheduling algorithms.
An Introduction to Psychological Statistics
We are constantly bombarded by information, and finding a way to filter that information in an objective way is crucial to surviving this onslaught with your sanity intact. This is what statistics, and logic we use in it, enables us to do. Through the lens of statistics, we learn to find the signal hidden in the noise when it is there and to know when an apparent trend or pattern is really just randomness. The study of statistics involves math and relies upon calculations of numbers. But it also relies heavily on how the numbers are chosen and how the statistics are interpreted.
The Data Renaissance: Analyzing the Disciplinary Effects of Big Data, Artificial Intelligence, and Beyond
The Data Renaissance delves into the complexities of data's role in various industries and its broader impact on society. It highlights the challenges in investigating data practices, citing examples like TikTok, where algorithms and data handling are closely guarded secrets. The content, contributed by students under the guidance of an expert, covers a wide range of topics, including the ethical aspects of generative AI in education and the workplace, and case studies reflecting real-world experiences. This evolving text, intended to be updated with each class, serves as a dynamic resource for educators and students alike, offering insights and discussion guides for an in-depth understanding of the ever-changing landscape of data in our digital age.
Statistical Analysis with The General Linear Model
This course is about a large and complex set of statistical methods tied together by a unifying conceptual framework known as “The General Linear Model” (GLM). This model can be used to answer an amazing variety of research questions within an inﬁnite number of diﬀerent experimental designs. Basically, the GLM can be used to test almost any hypothesis about a dependent variable (DV) that is measured numerically (e.g., height, income, IQ, age, time needed to run a 100-yard dash, grade point average, etc.; but not categorical DVs like eye color, sex, etc.). In a ﬁrst statistics course, students will have seen some special cases of the GLM without knowing it. For example, the various kinds of “t-tests” (one-sample, between-subjects, within-subjects, etc.) are special cases of the GLM. So are correlation, regression, and the Analysis of Variance (ANOVA). We will not assume any prior knowledge of these techniques, but students should realize, if the new methods seem familiar, that they are now seeing the big picture.
Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics
Mathematical definitions should be perfectly precise because they do not describe something which is observed out there in the world, since such descriptive definitions might have fuzzy edges. In biology, for example, whether a virus is considered “alive” could be subject to some debate: viruses have some of the characteristics of life, but not others. This makes a mathematician nervous.
You are exposed to statistics regularly. If you are a sports fan, then you have the statistics for your favorite player. If you are interested in politics, then you look at the polls to see how people feel about certain issues or candidates. If you are an environmentalist, then you research arsenic levels in the water of a town or analyze the global temperatures. If you are in the business profession, then you may track the monthly sales of a store or use quality control processes to monitor the number of defective parts manufactured. If you are in the health profession, then you may look at how successful a procedure is or the percentage of people infected with a disease. There are many other examples from other areas. To understand how to collect data and analyze it, you need to understand what the field of statistics is and the basic definitions.
From Algorithms to Z-Scores: Probabilistic and Statistical Modeling in Computer Science
ntroductory Statistics is designed for the one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean. Additional topics, examples, and ample opportunities for practice have been added to each chapter. The development choices for this textbook were made with the guidance of many faculty members who are deeply involved in teaching this course. These choices led to innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful, so that students can draw from it a working knowledge that will enrich their future studies and help them make sense of the world around them.
An Invitation to Statistics in Wasserstein Space
This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds).
This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired. In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks. Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals). Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
Quantitative Problem Solving in Natural Resources - Second Edition
This book is a collection of resources focused on solving quantitative problems that non-mathematicians interested in biology and environmental sciences may find compelling. It is not intended as a guide to be followed through a series of skills, but rather as a resource to support the problem-solving process and help lower conceptual and computational barriers along the way.
Quantitative Problem Solving in Natural Resources
This text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with in their disciplinary coursework and professional internships.
Theory and Applications of Ordered Fuzzy Numbers: A Tribute to Professor Witold Kosiński
The subject of this chapter is fuzzy sets and the basic issues related to them. The first section discusses concepts of sets: classic and fuzzy, and presents various ways of describing fuzzy sets. The second section is dedicated to t-norms, s-norms, and other terms associated with fuzzy sets. Subsequent sections describe the extension principle, fuzzy relations and their compositions, cylindrical extension and projection of a fuzzy set. The sixth section discusses fuzzy numbers and basic arithmetic operations on them. Finally, the last section summarizes the chapter.
This text is for an introductory level probability and statistics course with an intermediate algebra prerequisite. The focus of the text follows the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics Education (GAISE).
Statistical Thinking for the 21st Century
Statistical thinking is a way of understanding a complex world by describing it in relatively simple terms that nonetheless capture essential aspects of its structure, and that also provide us some idea of how uncertain we are about our knowledge. The foundations of statistical thinking come primarily from mathematics and statistics, but also from computer science, psychology, and other fields of study. We can distinguish statistical thinking from other forms of thinking that are less likely to describe the world accurately. In particular, human intuition often tries to answer the same questions that we can answer using statistical thinking, but often gets the answer wrong. For example, in recent years most Americans have reported that they think that violent crime was worse compared to the previous year (Pew Research Center). However, a statistical analysis of the actual crime data shows that in fact violent crime has steadily decreased since the 1990’s. Intuition fails us because we rely upon best guesses (which psychologists refer to as heuristics) that can often get it wrong. For example, humans often judge the prevalence of some event (like violent crime) using an availability heuristic – that is, how easily can we think of an example of violent crime. For this reason, our judgments of increasing crime rates may be more reflective of increasing news coverage, in spite of an actual decrease in the rate of crime. Statistical thinking provides us with the tools to more accurately understand the world and overcome the fallibility of human intuition.
Linear models are statistical models that play a crucial role in several fields of science and are of practical importance in statistics. The most typical type is the linear regression model. Many phenomena, such as those in biology, medicine, economics, management, geology, meteorology, agriculture and industry, can be approximately described with linear models. Thus, the further research and development of linear models is still a hot research topic.
The solution to many real-world problems lies in optimizing processes, parameters, or techniques, which requires dealing with immense search spaces. As such, finding solutions involves exhaustive methods to evaluate all possible solutions in the search for a global optimum.
Sebastián Ventura (editor). José María Luna (editor)
With Response Surface Methods - Theory, Applications, and Optimization Techniques, one can unlock the full potential of experimental designs. This comprehensive guide delves into the complexity of Response Surface Methodology (RSM), offering both foundational theories and cutting-edge applications. This book provides novices and experienced practitioners with the tools and knowledge required to optimize processes, enhance quality, and drive innovation. Through a mix of theoretical insights and practical case studies, one addresses how RSM can be applied across a diverse set of fields, including engineering, chemistry, biology, health care, and more.
Stochastic Processes: Theory and Applications
The aim of this special issue is to publish original research papers that cover recent advances in the theory and application of stochastic processes. There is especial focus on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics. Potential topics include, but are not limited
Zeifman, Alexander --- Korolev, Victor --- Sipin, Alexander