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Lord G: An Introduction to Stochastic
Modeling

An Introduction to Stochastic Modeling

The new edition of Biostatistics for Clinical and Public Health Research is the only introductory workbook to provide not only a concise overview of key statistical concepts but also step-by-step guidance on how to apply these through a range of software packages, including R, SAS, and Stata.

Biostatistics for Clinical and Public Health Research

This accessible book for graduate students and data scientists provides a solid background in probabilistic and statistical concepts relevant to data science. Emphasis is placed on practice, with examples throughout using real-world data that readers can implement from Python code available on the book's website.

Probability and Statistics for Data Science

This research monograph explores new frontiers in Markov chains. Although time-homogeneous Markov chains are well understood, this is not at all the case with time-inhomogeneous ones. The book, after a review on the classical theory of homogeneous chains, including the electrical network approach, introduces several new models which involve inhomogeneous chains as well as related new types of random walks (for example, "coin turning", "conservative" and "Rademacher" walk). Scaling limits, the breakdown of the classical limit theorems as well as recurrence and transience are investigated. The relationship with urn models is the subject of two chapters, providing additional connections to other parts of probability theory.

Random walks on random graphs are discussed as well, as an area where the method of electric networks is especially useful. This is illustrated by presenting random walks in random environments and random labyrinths.

The monograph puts emphasis on showing examples and open problems besides providing rigorous analysis of the models.

Several figures illustrate the main ideas, and a large number of exercises challenge the interested reader.

Coin-turning, Random Walks And Inhomogeneous Markov Chains

Probability for Deep Learning Quantum provides readers with the first book to address probabilistic methods in the deep learning environment and the quantum technological area simultaneously, by using a common platform: the Many-Sorted Algebra (MSA) view. While machine learning is created with a foundation of probability, probability is at the heart of quantum physics as well. It is the cornerstone in quantum applications. These applications include quantum measuring, quantum information theory, quantum communication theory, quantum sensing, quantum signal processing, quantum computing, quantum cryptography, and quantum machine learning. Although some of the probabilistic methods differ in machine learning disciplines from those in the quantum technologies, many techniques are very similar. Probability is introduced in the text rigorously, in Komogorov’s vision. It is however, slightly modified by developing the theory in a Many-Sorted Algebra setting. This algebraic construct is also used in showing the shared structures underlying much of both machine learning and quantum theory. Both deep learning and quantum technologies have several probabilistic and stochastic methods in common. These methods are described and illustrated using numerous examples within the text. Concepts in entropy are provided from a Shannon as well as a von-Neumann view. Singular value decomposition is applied in machine learning as a basic tool and presented in the Schmidt decomposition. Besides the in-common methods, Born’s rule as well as positive operator valued measures are described and illustrated, along with quasi-probabilities. Author Charles R. Giardina provides clear and concise explanations, accompanied by insightful and thought-provoking visualizations, to deepen your understanding and enable you to apply the concepts to real-world scenarios.

A Many-Sorted Algebra View

Probability for Deep Learning Quantum

Chapman and Hall/CRC Series on Statistics in Business and Economics

This book delves into scalable Bayesian statistical methods designed to tackle the challenges posed by big data. It explores a variety of divide-and-conquer and subsampling techniques. The book is an essential resource for graduate students, early-career statisticians, data analysts, and statistical software users and developers.

Bayesian Econometric Modelling for Big Data

The Converse of Bayes Theorem with Applications

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

Chapman & Hall/CRC Biostatistics Series

This book provides a comprehensive overview of the current trends, challenges, and opportunities in modernizing clinical trials, offering a roadmap for stakeholders in this evolving field. It provides actionable insights into the future of clinical trials and their role in bringing new therapies to market faster and more effectively.

Technological, Operational, and Regulatory Advances

Clinical Trial Modernization

This book guides the reader through power and sample size calculations for a variety of study outcomes and designs and illustrates their implementation in R. It is designed to be used as a learning tool for students as well as a resource for experienced statisticians and investigators.

This book guides the reader through power and sample size calculations for a variety of study outcomes and designs and illustrates their implementation in R. It is designed to be used as a learning tool for students as well as a resource for experienced statisticians and investigators.

Power and Sample Size in R

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

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

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Significant new challenges to the use of likelihood-based methods for inference have helped to generate considerable interest in alternative inference methods that are not based on a full likelihood specification. This book provides a comprehensive survey of likelihood methods in statistics, with an emphasis on developments to inference functions for use in complex data. These inference functions are usually motivated by considerations related to likelihood-type arguments and have a variety of names, including composite likelihood, quasi-likelihood and pseudo-likelihood.

Significant new challenges to the use of likelihood-based methods for inference have helped to generate considerable interest in alternative inference methods that are not based on a full likelihood specification. This book provides a comprehensive survey of likelihood methods in statistics, with an emphasis on developments to inference functions for use in complex data. These inference functions are usually motivated by considerations related to likelihood-type arguments and have a variety of names, including composite likelihood, quasi-likelihood and pseudo-likelihood.

Likelihood and its Extensions

An Introduction to Stochastic Modeling

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