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Prell M: What Are the Odds?

What Are the Odds?

A Statistical Guide to Certainty in an Uncertain World

This comprehensive compendium addresses a critical need in the AI and machine learning era by bridging foundational information theory (IT) concepts with practical applications in statistical learning. Unlike traditional IT textbooks, this volume emphasizes how IT principles, such as entropy and source coding, underpin modern machine learning techniques like cross-entropy, decision trees, and evidence-lower bounds.This unique book connects IT with probabilistic inference, illustrated through real-world applications, such as decoding LDPC codes for error correction. The inclusion of the Lea probabilistic programming package is particularly valuable for pedagogy, offering students a hands-on tool to solve numerical problems and reinforce theoretical concepts.The useful reference text benefits professionals, researchers, academics and students in the fields of calculus and probability, communications and information sciences.

Introduction To Information Theory And Probabilistic Inference, An

Meta-analysis Using R

Scaling (zooming in or out) is taking a close or distant view of an object. Infinite scaling (the scaling parameter tends to zero or infinity) may lead to a limit which is self-similar and much simpler than the original object. For instance, the classical Donsker's theorem says that all weakly dependent stationary processes with finite variance scale to Brownian motion at large scales. In the case of a random field indexed by two-dimensional parameter, both types of scaling can be anisotropic, meaning that the horizontal and vertical axes are scaled at different rate determined by the ratio γ&gt;0 of the scaling exponents along the axes. The natural questions under such scaling are whether the scaling limits exist for any γ&gt;0, and what are these limits are. The book tries to answer these questions. It introduces the concept of scaling transition and discusses its existence for a natural class of planar random fields including Gaussian, linear and some nonlinear ones. The scaling limits are identified and exhibit a surprising trichitomy at a critical point γ0, with 'unbalanced' limits having unusual path properties and dependence structure along one of the coordinate axes. Scaling transition occurs in applied sciences (telecommunications and econometrics) when aggregating independent processes with long-range dependence in which case 'unbalanced' limits are classical Gaussian or stable random fields.

Anisotropic Scaling Of Random Fields With Long-range Dependence: Scaling Limits Of Random Fields With Applications

From the coauthor of Algorithms to Live By, an exploration of the quest to use mathematics to describe the ways we think, from its origins three hundred years ago to the ideas behind modern AI systems and the ways in which they still differ from human minds.Everyone has a basic understanding of how the physical world works. We learn about physics and chemistry in school, letting us explain the world around us in terms of concepts like force, acceleration, and gravity-the Laws of Nature. But we don't have the same fluency with concepts needed to understand the world inside us-the Laws of Thought. While the story of how mathematics has been used to reveal the mysteries of the universe is familiar, the story of how it has been used to study the mind is not.There is no one better to tell that story than Tom Griffiths, the head of Princeton's AI Lab and a renowned expert in the field of cognitive science. In this groundbreaking book, he explains the three major approaches to formalizing thought-rules and symbols, neural networks, and probability and statistics-introducing each idea through the stories of the people behind it. As informed conversations about thought, language, and learning become ever more pressing in the age of AI, The Laws of Thought is an essential read for anyone interested in the future of technology.

The Quest for a Mathematical Theory of the Mind

The Laws of Thought

Sustainable Supply Chain Management: Computational Approaches and Modelling provides a comprehensive understanding of how computational approaches can be leveraged to address the challenges associated with sustainable supply chain management. It offers insights into emerging and advanced modelling techniques to optimize supply chain operations while considering environmental, social, and economic factors. This book will be a valuable resource for researchers, practitioners, and policymakers interested in understanding and implementing sustainable supply chain management practices through computational approaches and modelling. This book helps researchers understand the opportunities, challenges, and solutions by developing innovative computational tools and techniques to integrate sustainability considerations into supply chain decision-making processes.

Computational Approaches and Modelling

Sustainable Supply Chain Management

Series On Analysis, Applications And Computation

The book is devoted to rigorous mathematical results on discrete nonlinear Schrödinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations emerge as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there is necessary material from the spectral theory of discrete Schrödinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.

Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability

The book is devoted to contemporary variance reduction methods for Monte Carlo and Markov Chain (MCMC) with Machine Learning and Finance applications. We present new approaches based on martingale representations, and Stein control variates besides the standard techniques. In addition, the book focuses on developing new variance reduction algorithms in MCMC and their theoretical analysis. Readers will find numerical examples that illustrate all proposed algorithms.

Advanced Variance Reduction Techniques For Mcmc

Huge Numbers

This book illustrates how the choice of relevant data collection and data analysis techniques is critical for a sound and objective description of the complexity of space-time patterns and processes in ecology and the aquatic sciences. It reviews the concept of complexity in a general ecological context, before introducing a unifying definition of complexity in marine ecology. The book shows that convincing results can arise from very simple, sound, and well-thought-out approaches. The authors underline the risks related to modern techniques of data assimilation that can lead to data inundation, a loss of focus, and ultimately an erroneous scientific approach.

A Practical Guide to Avoid Becoming a Mistaken Scientist

Interpreting Ecological Complexity

This book presents a comprehensive treatment of pricing and hedging soccer betting contracts using the modern techniques of probability, statistics, finance, and portfolio management. It introduces betting in general and then addresses the probabilistic intuition needed in the more complex world of soccer betting. The author presents an innovative perspective by thinking about betting odds in terms of the expected number of goals of both teams. In addition, when the betting market is in play, the book treats betting before the game and during the game separately.

Science of Soccer Statistics

Soccermetrics

Best Practices for Scaling and Optimizing Apache Spark

High Performance Spark

What Are the Odds?

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