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21 results in Statistics and Probability

Page 1 of 2

All of Regression
  • Isabella Verdinelli, Larry Wasserman
  • Published online:
    08 May 2026
    Print publication:
    04 June 2026
  • This comprehensive modern look at regression covers a wide range of topics and relevant contemporary applications, going well beyond the topics covered in most introductory books. With concision and clarity, the authors present linear regression, nonparametric regression, classification, logistic and Poisson regression, high-dimensional regression, quantile regression, conformal prediction and causal inference. There are also brief introductions to neural nets, deep learning, random effects, survival analysis, graphical models and time series. Suitable for advanced undergraduate and beginning graduate students, the book will also serve as a useful reference for researchers and practitioners in data science, machine learning, and artificial intelligence who want to understand modern methods for data analysis.

A Practical Guide to Time Series Analysis
  • Suzanna Linn, Matthew J. Lebo, Clayton Webb
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    07 May 2026
  • Understanding change over time is a critical component of social science. However, data measured over time – time series – requires their own set of statistical and inferential tools. In this book, Suzanna Linn, Matthew Lebo, and Clayton Webb explain the most commonly used time series models and demonstrate their applications using examples. The guide outlines the steps taken to identify a series, make determinations about exogeneity/endogeneity, and make appropriate modelling decisions and inferences. Detailing challenges and explanations of key techniques not covered in most time series textbooks, the authors show how navigating between data and models, deliberately and transparently, allows researchers to clearly  explain their statistical analyses to a broad audience.

Bias!
  • How Systemic Error Threatens Biomedical Research
  • Michael B. Bracken
  • Published online:
    22 April 2026
    Print publication:
    07 May 2026
  • An intricate landscape of bias permeates biomedical research. In this groundbreaking exploration the myriad sources of bias shaping research outcomes, from cognitive biases inherent in researchers to the selection of study subjects and data interpretation, are examined in detail. With a focus on randomized controlled trials, pharmacologic studies, genetic research, animal studies, and pandemic analyses, it illuminates how bias distorts the quest for scientific truth. Historical and contemporary examples vividly illustrate the impact of biases across research domains. Offering insights on recognizing and mitigating bias, this comprehensive work equips scientists and research teams with tools to navigate the complex terrain of biased research practices. A must-read for anyone seeking a deeper understanding of the critical role biases play in shaping the reliability and reproducibility of biomedical research.

Risk Measures
  • An Introduction to the Mathematical Theory
  • Ilya Molchanov, Johanna Ziegel
  • Published online:
    26 February 2026
    Print publication:
    19 February 2026
  • Providing comprehensive yet accessible coverage, this is the first graduate-level textbook dedicated to the mathematical theory of risk measures. It explains how economic and financial principles result in a profound mathematical theory that allows us to quantify risk in monetary terms, giving rise to risk measures. Each chapter is designed to match the length of one or two lectures, covering the core theory in a self-contained manner, with exercises included in every chapter. Additional material sections then provide further background and insights for those looking to delve deeper. This two-layer modular design makes the book suitable as the basis for diverse lecture courses of varying length and level, and a valuable resource for researchers.

Elements of Structural Equation Models (SEMs)
  • Kenneth A. Bollen
  • Published online:
    05 February 2026
    Print publication:
    19 February 2026
  • Elements of Structural Equation Models (SEMs) blends theoretical foundations with practical applications, serving as both a learning tool and a lasting reference. Synthesizing material from diverse sources, including the author's own contributions, it provides a rigorous yet accessible guide for graduate students, faculty, and researchers across social, behavioral, health, and data sciences. The book covers essential SEM concepts – model assumptions, identification, estimation, and diagnostics – while also addressing advanced topics often overlooked, such as Bayesian SEMs, model-implied instrumental variables, and categorical variables. Readers will gain insights into missing data, longitudinal models, and comparisons with Directed Acyclic Graphs (DAGs). By presenting complex technical content in a clear, structured way, this authoritative resource deepens readers' understanding of SEMs, making it an indispensable guide for both newcomers and experts seeking a definitive treatment of the field.

High-Dimensional Probability
  • An Introduction with Applications in Data Science
  • 2nd edition
  • Roman Vershynin
  • Published online:
    30 January 2026
    Print publication:
    19 February 2026
  • 'High-Dimensional Probability,' winner of the 2019 PROSE Award in Mathematics, offers an accessible and friendly introduction to key probabilistic methods for mathematical data scientists. Streamlined and updated, this second edition integrates theory, core tools, and modern applications. Concentration inequalities are central, including classical results like Hoeffding's and Chernoff's inequalities, and modern ones like the matrix Bernstein inequality. The book also develops methods based on stochastic processes – Slepian's, Sudakov's, and Dudley's inequalities, generic chaining, and VC-based bounds. Applications include covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, and machine learning. New to this edition are 200 additional exercises, alongside extra hints to assist with self-study. Material on analysis, probability, and linear algebra has been reworked and expanded to help bridge the gap from a typical undergraduate background to a second course in probability.

Play of Chance and Purpose
  • An Invitation to Probability, Statistics, and Stochasticity Using Simulations and Projects
  • Amrik Sen
  • Published online:
    13 January 2026
    Print publication:
    31 May 2026
  • Play of Chance and Purpose emphasizes learning probability, statistics, and stochasticity by developing intuition and fostering imagination as a pedagogical approach. This book is meant for undergraduate and graduate students of basic sciences, applied sciences, engineering, and social sciences as an introduction to fundamental as well as advanced topics. The text has evolved out of the author's experience of teaching courses on probability, statistics, and stochastic processes at both undergraduate and graduate levels in India and the United States. Readers will get an opportunity to work on several examples from real-life applications and pursue projects and case-study analyses as capstone exercises in each chapter. Many projects involve the development of visual simulations of complex stochastic processes. This will augment the learners' comprehension of the subject and consequently train them to apply their learnings to solve hitherto unseen problems in science and engineering.

Statistics for Chemical Engineers
  • From Data to Models to Decisions
  • Victor M. Zavala
  • Published online:
    12 December 2025
    Print publication:
    25 September 2025
  • Build a firm foundation for studying statistical modelling, data science, and machine learning with this practical introduction to statistics, written with chemical engineers in mind. It introduces a data–model–decision approach to applying statistical methods to real-world chemical engineering challenges, establishes links between statistics, probability, linear algebra, calculus, and optimization, and covers classical and modern topics such as uncertainty quantification, risk modelling, and decision-making under uncertainty. Over 100 worked examples using Matlab and Python demonstrate how to apply theory to practice, with over 70 end-of-chapter problems to reinforce student learning, and key topics are introduced using a modular structure, which supports learning at a range of paces and levels. Requiring only a basic understanding of calculus and linear algebra, this textbook is the ideal introduction for undergraduate students in chemical engineering, and a valuable preparatory text for advanced courses in data science and machine learning with chemical engineering applications.

Gaussian Free Field and Liouville Quantum Gravity
  • Nathanaël Berestycki, Ellen Powell
  • Published online:
    20 November 2025
    Print publication:
    04 December 2025
  • In this comprehensive volume, the authors introduce some of the most important recent developments at the intersection of probability theory and mathematical physics, including the Gaussian free field, Gaussian multiplicative chaos and Liouville quantum gravity. This is the first book to present these topics using a unified approach and language, drawing on a large array of multi-disciplinary techniques. These range from the combinatorial (discrete Gaussian free field, random planar maps) to the geometric (culminating in the path integral formulation of Liouville conformal field theory on the Riemann sphere) via the complex analytic (based on the couplings between Schramm–Loewner evolution and the Gaussian free field). The arguments (currently scattered over a vast literature) have been streamlined and the exposition very carefully thought out to present the theory as much as possible in a reader-friendly, pedagogical yet rigorous way, suitable for graduate students as well as researchers.

Testing and the Paradoxes of Fairness
  • Howard Wainer, Daniel H. Robinson
  • Published online:
    10 October 2025
    Print publication:
    30 October 2025
  • How can admissions officers, employers, and scholarship committees maximize the accuracy of prediction of individual performance while minimizing adverse impact due to group differences? Testing offers a straightforward solution to the first half of this problem. Tests are the best way to predict how someone will perform in school, in the military, in medicine, or while controlling airline traffic and flying a plane. Tests are also useful beyond personnel selection, such as for selection of a college major or courses. However, the other side of this problem is more complex. Using tests is always accompanied by group differences that could result in continued systemic discrimination by limiting opportunities for those who are marginalized. This book charts an approach to using tests that incorporates evidence, transparency, and societal values to maximize efficiency and fairness.

Multivariable Analysis
  • A Practical Guide for Clinicians and Public Health Researchers
  • 4th edition
  • Mitchell H. Katz
  • Published online:
    09 October 2025
    Print publication:
    23 October 2025
  • Now in its fourth edition, this best-selling, highly praised text has been fully revised and updated with expanded sections on propensity analysis, sensitivity analysis, and emulation trials. As before, it focuses on easy-to follow explanations of complicated multivariable techniques including logistic regression, proportional hazards analysis, and Poisson regression. The perfect introduction for medical researchers, epidemiologists, public health practitioners, and health service researchers, this book describes how to preform and interpret multivariable analysis, using plain language rather than mathematical formulae. It takes advantage of the availability of user-friendly software that allow novices to conduct complex analysis without programming experience; ensuring that these analyses are set up and interpreted correctly. Numerous tables, graphs, and tips help to demystify the process of performing multivariable analysis. The text is illustrated with many up-to-date examples from the published literature that enable readers to model their analyses after well conducted research, increasing chances of top-tier publication.

Hands-On Network Machine Learning with Python
  • Eric W. Bridgeford, Alexander R. Loftus, Joshua T. Vogelstein
  • Published online:
    23 September 2025
    Print publication:
    18 September 2025
  • Bridging theory and practice in network data analysis, this guide offers an intuitive approach to understanding and analyzing complex networks. It covers foundational concepts, practical tools, and real-world applications using Python frameworks including NumPy, SciPy, scikit-learn, graspologic, and NetworkX. Readers will learn to apply network machine learning techniques to real-world problems, transform complex network structures into meaningful representations, leverage Python libraries for efficient network analysis, and interpret network data and results. The book explores methods for extracting valuable insights across various domains such as social networks, ecological systems, and brain connectivity. Hands-on tutorials and concrete examples develop intuition through visualization and mathematical reasoning. The book will equip data scientists, students, and researchers in applications using network data with the skills to confidently tackle network machine learning projects, providing a robust toolkit for data science applications involving network-structured data.

Probability Theory for Quantitative Scientists
  • Luca Leuzzi, Enzo Marinari, Giorgio Parisi
  • Published online:
    24 July 2025
    Print publication:
    14 August 2025
  • Based on the long-running Probability Theory course at the Sapienza University of Rome, this book offers a fresh and in-depth approach to probability and statistics, while remaining intuitive and accessible in style. The fundamentals of probability theory are elegantly presented, supported by numerous examples and illustrations, and modern applications are later introduced giving readers an appreciation of current research topics. The text covers distribution functions, statistical inference and data analysis, and more advanced methods including Markov chains and Poisson processes, widely used in dynamical systems and data science research. The concluding section, 'Entropy, Probability and Statistical Mechanics' unites key concepts from the text with the authors' impressive research experience, to provide a clear illustration of these powerful statistical tools in action. Ideal for students and researchers in the quantitative sciences this book provides an authoritative account of probability theory, written by leading researchers in the field.

A Logic of Populism
  • India and Its States
  • Srikrishna Ayyangar
  • Published online:
    05 July 2025
    Print publication:
    10 July 2025
  • What makes populism both a threat and a corrective to democracy in India, setting it apart from other contexts? A Logic of Populism explores this question using a novel set-theoretic methodology and a comprehensive study of populist leaders across Indian states. It defines populists as those who draw boundaries dividing people, while democratic institutions shape these divisions' political significance. Populists create fractures, yet democratic engagement channels these conflicts toward the common good. This book is essential for those seeking to understand Indian democracy and populism's role in political modernization beyond Western perspectives. It is particularly valuable for researchers in qualitative methodologies and theory-building in the Social Sciences. By conceptualizing populism as a defining force in contemporary public affairs, the book offers crucial insights into democracy's evolving landscape in India, making it a significant contribution to political studies and governance discourse.

Probability, Geometry and Integrable Systems
  • Edited by Mark Pinsky, Bjorn Birnir
  • Mathematical Sciences Research Institute
  • Published online:
    27 June 2025
    Print publication:
    17 March 2008
  • The three main themes of this book, probability theory, differential geometry, and the theory of integrable systems, reflect the broad range of mathematical interests of Henry McKean, to whom it is dedicated. Written by experts in probability, geometry, integrable systems, turbulence, and percolation, the seventeen papers included here demonstrate a wide variety of techniques that have been developed to solve various mathematical problems in these areas. The topics are often combined in an unusual and interesting fashion to give solutions outside of the standard methods. The papers contain some exciting results and offer a guide to the contemporary literature on these subjects.

Modern Signal Processing
  • Edited by Daniel N. Rockmore, Dennis M. Healy, Jr
  • Mathematical Sciences Research Institute
  • Published online:
    25 June 2025
    Print publication:
    05 April 2004
  • Signal processing is everywhere in modern technology. Its mathematical basis and many areas of application are the subject of this book, based on a series of graduate-level lectures held at the Mathematical Sciences Research Institute. Emphasis is on challenges in the subject, particular techniques adapted to particular technologies, and certain advances in algorithms and theory. The book covers two main areas: computational harmonic analysis, envisioned as a technology for efficiently analysing real data using inherent symmetries; and the challenges inherent in the acquisition, processing and analysis of images and sensing data in general [EMDASH] ranging from sonar on a submarine to a neuroscientist's fMRI study.

Probability and Statistics for Data Science
  • Carlos Fernandez-Granda
  • Published online:
    19 June 2025
    Print publication:
    03 July 2025
  • This self-contained guide introduces two pillars of data science, probability theory, and statistics, side by side, in order to illuminate the connections between statistical techniques and the probabilistic concepts they are based on. The topics covered in the book include random variables, nonparametric and parametric models, correlation, estimation of population parameters, hypothesis testing, principal component analysis, and both linear and nonlinear methods for regression and classification. Examples throughout the book draw from real-world datasets to demonstrate concepts in practice and confront readers with fundamental challenges in data science, such as overfitting, the curse of dimensionality, and causal inference. Code in Python reproducing these examples is available on the book's website, along with videos, slides, and solutions to exercises. This accessible book is ideal for undergraduate and graduate students, data science practitioners, and others interested in the theoretical concepts underlying data science methods.

Spatial Analysis
  • A Guide for Ecologists
  • 3rd edition
  • Mark R. T. Dale, Marie-Josée Fortin
  • Published online:
    19 June 2025
    Print publication:
    03 July 2025
  • Designed for researchers in ecology at all levels and career stages, from students and postdoctoral fellows to seasoned professionals, this third edition reflects the significant advances in quantitative analysis of the past decade. It provides updated examples and methods, with reduced emphasis on older techniques that have seen limited use in recent ecological literature. The authors cover new and emerging approaches, including Hierarchical Bayesian analysis and spatio-temporal methods. A key feature is the integration of ecological and statistical concepts, highlighting the critical role that this type of analysis plays in ecological understanding. The book provides up-to-date summaries of methodological advancements in spatial and spatio-temporal analysis, along with insights into future developments in areas such as spatial graphs, multi-level networks, and machine learning applications. It also offers practical examples and guidance to help researchers select, apply, and interpret the appropriate methods.

Random Matrix Theory, Interacting Particle Systems, and Integrable Systems
  • Edited by Percy Deift, Peter Forrester
  • Mathematical Sciences Research Institute
  • Published online:
    29 May 2025
    Print publication:
    15 December 2014
  • Random matrix theory is at the intersection of linear algebra, probability theory and integrable systems, and has a wide range of applications in physics, engineering, multivariate statistics and beyond. This volume is based on a Fall 2010 MSRI program which generated the solution of long-standing questions on universalities of Wigner matrices and beta-ensembles and opened new research directions especially in relation to the KPZ universality class of interacting particle systems and low-rank perturbations. The book contains review articles and research contributions on all these topics, in addition to other core aspects of random matrix theory such as integrability and free probability theory. It will give both established and new researchers insights into the most recent advances in the field and the connections among many subfields.

Partially Observed Markov Decision Processes
  • Filtering, Learning and Controlled Sensing
  • 2nd edition
  • Vikram Krishnamurthy
  • Published online:
    16 May 2025
    Print publication:
    05 June 2025
  • Covering formulation, algorithms and structural results and linking theory to real-world applications in controlled sensing (including social learning, adaptive radars and sequential detection), this book focuses on the conceptual foundations of partially observed Markov decision processes (POMDPs). It emphasizes structural results in stochastic dynamic programming, enabling graduate students and researchers in engineering, operations research, and economics to understand the underlying unifying themes without getting weighed down by mathematical technicalities. In light of major advances in machine learning over the past decade, this edition includes a new Part V on inverse reinforcement learning as well as a new chapter on non-parametric Bayesian inference (for Dirichlet processes and Gaussian processes), variational Bayes and conformal prediction.

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