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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

Chapman & Hall/CRC Biostatistics Series

Age-Period-Cohort Models

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

This book presents an overview of the diverse literature on change-point methodology and describes some unifying themes and recent breakthroughs. It can be used as a second-year Ph.D. level course in statistics. It is expected to be useful to researchers and graduate students, not only in statistics but also in engineering, biomedicine, economics and finance.

This book presents an overview of the diverse literature on change-point methodology and describes some unifying themes and recent breakthroughs. It can be used as a second-year Ph.D. level course in statistics. It is expected to be useful to researchers and graduate students, not only in statistics but also in engineering, biomedicine, economics and finance.

Change-point Methodology and Applications

Chapman & Hall/CRC Interdisciplinary Statistics

An introduction to a new paradigm in social, technological, and scientific discourse, this book presents an overview of statistical methods for describing, modeling, and inferring biological networks using genomic and other types of data. It covers a large variety of modern statistical techniques, such as sparse graphical models, state space models, Boolean networks, and hidden Markov models. The authors address gene transcription data, microRNAs, ChIP-chip, and RNAi data. Along with end-of-chapter exercises, the text includes many real-world examples with implementations using a dedicated R package.

An introduction to a new paradigm in social, technological, and scientific discourse, this book presents an overview of statistical methods for describing, modeling, and inferring biological networks using genomic and other types of data. It covers a large variety of modern statistical techniques, such as sparse graphical models, state space models, Boolean networks, and hidden Markov models. The authors address gene transcription data, microRNAs, ChIP-chip, and RNAi data. Along with end-of-chapter exercises, the text includes many real-world examples with implementations using a dedicated R package.

How to Infer Networks from Data

Statistics for Biological Networks

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.

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 unique compendium develops a general approach to building models of economic and financial processes, with a focus on statistical learning techniques that scale to large data sets. It introduces the key elements of a parametric statistical model: likelihood, prior, and posterior, and show how to use them to make predictions.The book covers classical techniques such as multiple regression and the Kalman filter in a clear, accessible style that has been popular with students, but also includes detailed treatments of state-of-the-art models, highlighting tree-based methods, support vector machines and kernel methods, deep learning, and reinforcement learning. Theories are supplemented by real-world examples.This reference text is useful for undergraduate, graduate and even PhD students in quantitative finance, and also to practitioners who are facing the reality that data science and machine learning are disrupting the industry.

Statistical Machine Learning With Applications In Finance

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

Probability theory is a discipline that studies the quantitative regularity of random phenomena. The fact that random phenomena arise, especially in the era of big data and artificial intelligence, determines the importance of this discipline. This volume introduces various concepts that quantitatively describe random phenomena, including probability, random variables, distribution functions, density functions, mathematical expectations, variances, moments, and characteristic functions. It finishes off by presenting probability limit theory, including various convergences.Throughout the volume, great importance is attached to the elaboration of probability thoughts. For this reason, some practical examples to illustrate the introduced concept are always used. In order to meet the needs of different levels of readers, there is a section on Supplements and Notes at the end of each chapter to enhance and expand the content in the body of the textbook. This volume contains a large number of problems of varying levels for the reader with the purpose to review, consolidate, deepen and expand their knowledge.As the only branch of mathematics that studies the quantitative regularity of random phenomena, probability theory has not only theoretical significance, but it is also a main theoretical basis of mathematical statistics. Therefore, it will be of interest to scholars from other disciplines related to random phenomena.

Probability Theory: An Elementary Course

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.

What Are the Odds?

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