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101 results in Statistical theory and methods

Page 1 of 6

Hands-On Network Machine Learning with Python
  • Eric W. Bridgeford, Alexander R. Loftus, Joshua T. Vogelstein
  • Coming soon
  • Expected online publication date:
    August 2025
    Print publication:
    31 August 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 and Statistics for Data Science
  • Carlos Fernandez-Granda
  • Coming soon
  • Expected online publication date:
    July 2025
    Print publication:
    31 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.

Dependence Models via Hierarchical Structures
  • Luis E. Nieto-Barajas
  • Published online:
    20 March 2025
    Print publication:
    27 March 2025
  • Bringing together years of research into one useful resource, this text empowers the reader to creatively construct their own dependence models. Intended for senior undergraduate and postgraduate students, it takes a step-by-step look at the construction of specific dependence models, including exchangeable, Markov, moving average and, in general, spatio-temporal models. All constructions maintain a desired property of pre-specifying the marginal distribution and keeping it invariant. They do not separate the dependence from the marginals and the mechanisms followed to induce dependence are so general that they can be applied to a very large class of parametric distributions. All the constructions are based on appropriate definitions of three building blocks: prior distribution, likelihood function and posterior distribution, in a Bayesian analysis context. All results are illustrated with examples and graphical representations. Applications with data and code are interspersed throughout the book, covering fields including insurance and epidemiology.

Information Theory
  • From Coding to Learning
  • Yury Polyanskiy, Yihong Wu
  • Published online:
    09 January 2025
    Print publication:
    02 January 2025
  • This enthusiastic introduction to the fundamentals of information theory builds from classical Shannon theory through to modern applications in statistical learning, equipping students with a uniquely well-rounded and rigorous foundation for further study. Introduces core topics such as data compression, channel coding, and rate-distortion theory using a unique finite block-length approach. With over 210 end-of-part exercises and numerous examples, students are introduced to contemporary applications in statistics, machine learning and modern communication theory. This textbook presents information-theoretic methods with applications in statistical learning and computer science, such as f-divergences, PAC Bayes and variational principle, Kolmogorov's metric entropy, strong data processing inequalities, and entropic upper bounds for statistical estimation. Accompanied by a solutions manual for instructors, and additional standalone chapters on more specialized topics in information theory, this is the ideal introductory textbook for senior undergraduate and graduate students in electrical engineering, statistics, and computer science.

Brownian Motion, the Fredholm Determinant, and Time Series Analysis
  • Katsuto Tanaka
  • Published online:
    19 December 2024
    Print publication:
    02 January 2025
  • Brownian motion is an important topic in various applied fields where the analysis of random events is necessary. Introducing Brownian motion from a statistical viewpoint, this detailed text examines the distribution of quadratic plus linear or bilinear functionals of Brownian motion and demonstrates the utility of this approach for time series analysis. It also offers the first comprehensive guide on deriving the Fredholm determinant and the resolvent associated with such statistics. Presuming only a familiarity with standard statistical theory and the basics of stochastic processes, this book brings together a set of important statistical tools in one accessible resource for researchers and graduate students. Readers also benefit from online appendices, which provide probability density graphs and solutions to the chapter problems.

Introduction to Probability and Statistics for Data Science
  • with R
  • Steven E. Rigdon, Ronald D. Fricker, Jr, Douglas C. Montgomery
  • Published online:
    13 December 2024
    Print publication:
    14 November 2024
  • Introduction to Probability and Statistics for Data Science provides a solid course in the fundamental concepts, methods and theory of statistics for students in statistics, data science, biostatistics, engineering, and physical science programs. It teaches students to understand, use, and build on modern statistical techniques for complex problems. The authors develop the methods from both an intuitive and mathematical angle, illustrating with simple examples how and why the methods work. More complicated examples, many of which incorporate data and code in R, show how the method is used in practice. Through this guidance, students get the big picture about how statistics works and can be applied. This text covers more modern topics such as regression trees, large scale hypothesis testing, bootstrapping, MCMC, time series, and fewer theoretical topics like the Cramer-Rao lower bound and the Rao-Blackwell theorem. It features more than 250 high-quality figures, 180 of which involve actual data. Data and R are code available on our website so that students can reproduce the examples and do hands-on exercises.

Experimental Sociology
  • Outline of a Scientific Field
  • Davide Barrera, Klarita Gërxhani, Bernhard Kittel, Luis Miller, Tobias Wolbring
  • Published online:
    23 November 2024
    Print publication:
    21 November 2024
  • Experiments have gained prominence in sociology in recent years. Increased interest in testing causal theories through experimental designs has ignited a debate about which experimental designs can facilitate scientific progress in sociology. This book discusses the implications of research interests for the design of experiments, identifies points of commonality and disagreement among the different perspectives within sociology, and elaborates on the rationales of each. It helps experimental sociologists find appropriate designs for answering specific research questions while alerting them to the challenges. Offering more than just a guide, this book explores both the historical roots of experimental sociology and the cutting-edge techniques of rigorous sociology. It concludes with a tantalizing peek into the future and provides a roadmap to the exciting prospects and uncharted territories of experimental sociology.

Polls, Pollsters, and Public Opinion
  • A Guide for Decision-Makers
  • Clifford Young, Kathryn Ziemer
  • Published online:
    01 November 2024
    Print publication:
    04 July 2024
  • A vast literature exists on theories of public opinion - how to measure, analyze, predict, and influence it; however, there is no synthesis of best practices for interpreting public opinion: existing knowledge is disparate and spread across many disciplines. Polls, Pollsters, and Public Opinion presents a systematic analytical approach for understanding, predicting, and engaging public opinion. It tells the story through the eyes of the pollster and draws an analytical road map for examining public opinion, both conceptually and practically. Providing a theoretical and conceptual foundation, as well as debunking popular myths, this book delves into the science of polling, offering tools analysts can use to assess the quality of polls. It also introduces methods that can be used to predict elections and other socio-political outcomes while understanding the nuances of messaging, engaging, and moving public opinion.

Active Statistics
  • Stories, Games, Problems, and Hands-on Demonstrations for Applied Regression and Causal Inference
  • Andrew Gelman, Aki Vehtari
  • Published online:
    07 March 2024
    Print publication:
    14 March 2024
  • This book provides statistics instructors and students with complete classroom material for a one- or two-semester course on applied regression and causal inference. It is built around 52 stories, 52 class-participation activities, 52 hands-on computer demonstrations, and 52 discussion problems that allow instructors and students to explore in a fun way the real-world complexity of the subject. The book fosters an engaging 'flipped classroom' environment with a focus on visualization and understanding. The book provides instructors with frameworks for self-study or for structuring the course, along with tips for maintaining student engagement at all levels, and practice exam questions to help guide learning. Designed to accompany the authors' previous textbook Regression and Other Stories, its modular nature and wealth of material allow this book to be adapted to different courses and texts or be used by learners as a hands-on workbook.

Polling at a Crossroads
  • Rethinking Modern Survey Research
  • Michael A. Bailey
  • Published online:
    29 February 2024
    Print publication:
    07 March 2024
  • Survey research is in a state of crisis. People have become less willing to respond to polls and recent misses in critical elections have undermined the field's credibility. Pollsters have developed many tools for dealing with the new environment, an increasing number of which rely on risky opt-in samples. Virtually all of these tools require that respondents in each demographic category are a representative sample of all people in each demographic category, something that is unlikely to be reliably true. Polling at a Crossroads moves beyond such strong limitations, providing tools that work even when survey respondents are unrepresentative in complex ways. This book provides case studies that show how to avoid underestimating Trump support and how conventional polls exaggerate partisan differences. This book also helps us think in clear and sometimes counterintuitive ways and points toward simple, low-cost changes that can better address contemporary polling challenges.

Generalized Additive Models for Location, Scale and Shape
  • A Distributional Regression Approach, with Applications
  • Mikis D. Stasinopoulos, Thomas Kneib, Nadja Klein, Andreas Mayr, Gillian Z. Heller
  • Published online:
    22 February 2024
    Print publication:
    29 February 2024
  • An emerging field in statistics, distributional regression facilitates the modelling of the complete conditional distribution, rather than just the mean. This book introduces generalized additive models for location, scale and shape (GAMLSS) – one of the most important classes of distributional regression. Taking a broad perspective, the authors consider penalized likelihood inference, Bayesian inference, and boosting as potential ways of estimating models and illustrate their usage in complex applications. Written by the international team who developed GAMLSS, the text's focus on practical questions and problems sets it apart. Case studies demonstrate how researchers in statistics and other data-rich disciplines can use the model in their work, exploring examples ranging from fetal ultrasounds to social media performance metrics. The R code and data sets for the case studies are available on the book's companion website, allowing for replication and further study.

Interaction Models
  • Specification and Interpretation
  • William Roberts Clark, Matt Golder
  • Published online:
    02 November 2023
    Print publication:
    16 November 2023
  • The radical interdependence between humans who live together makes virtually all human behavior conditional. The behavior of individuals is conditional upon the expectations of those around them, and those expectations are conditional upon the rules (institutions) and norms (culture) constructed to monitor, reward, and punish different behaviors. As a result, nearly all hypotheses about humans are conditional – conditional upon the resources they possess, the institutions they inhabit, or the cultural practices that tell them how to behave. Interaction Models provides a stand-alone, accessible overview of how interaction models, which are frequently used across the social and natural sciences, capture the intuition behind conditional claims and context dependence. It also addresses the simple specification and interpretation errors that are, unfortunately, commonplace. By providing a comprehensive and unified introduction to the use and critical evaluation of interaction models, this book shows how they can be used to test theoretically-derived claims of conditionality.

Time Series for Data Scientists
  • Data Management, Description, Modeling and Forecasting
  • Juana Sanchez
  • Published online:
    01 June 2023
    Print publication:
    11 May 2023
  • Learn by doing with this user-friendly introduction to time series data analysis in R. This book explores the intricacies of managing and cleaning time series data of different sizes, scales and granularity, data preparation for analysis and visualization, and different approaches to classical and machine learning time series modeling and forecasting. A range of pedagogical features support students, including end-of-chapter exercises, problems, quizzes and case studies. The case studies are designed to stretch the learner, introducing larger data sets, enhanced data management skills, and R packages and functions appropriate for real-world data analysis. On top of providing commented R programs and data sets, the book's companion website offers extra case studies, lecture slides, videos and exercise solutions. Accessible to those with a basic background in statistics and probability, this is an ideal hands-on text for undergraduate and graduate students, as well as researchers in data-rich disciplines

Data Management for Social Scientists
  • From Files to Databases
  • Nils B. Weidmann
  • Published online:
    03 March 2023
    Print publication:
    09 March 2023
  • The 'data revolution' offers many new opportunities for research in the social sciences. Increasingly, social and political interactions can be recorded digitally, leading to vast amounts of new data available for research. This poses new challenges for organizing and processing research data. This comprehensive introduction covers the entire range of data management techniques, from flat files to database management systems. It demonstrates how established techniques and technologies from computer science can be applied in social science projects, drawing on a wide range of different applied examples. This book covers simple tools such as spreadsheets and file-based data storage and processing, as well as more powerful data management software like relational databases. It goes on to address advanced topics such as spatial data, text as data, and network data. This book is one of the first to discuss questions of practical data management specifically for social science projects. This title is also available as Open Access on Cambridge Core.

The Conway–Maxwell–Poisson Distribution
  • Kimberly F. Sellers
  • Published online:
    02 March 2023
    Print publication:
    09 March 2023
  • While the Poisson distribution is a classical statistical model for count data, the distributional model hinges on the constraining property that its mean equal its variance. This text instead introduces the Conway-Maxwell-Poisson distribution and motivates its use in developing flexible statistical methods based on its distributional form. This two-parameter model not only contains the Poisson distribution as a special case but, in its ability to account for data over- or under-dispersion, encompasses both the geometric and Bernoulli distributions. The resulting statistical methods serve in a multitude of ways, from an exploratory data analysis tool, to a flexible modeling impetus for varied statistical methods involving count data. The first comprehensive reference on the subject, this text contains numerous illustrative examples demonstrating R code and output. It is essential reading for academics in statistics and data science, as well as quantitative researchers and data analysts in economics, biostatistics and other applied disciplines.

Exponential Families in Theory and Practice
  • Bradley Efron
  • Published online:
    25 November 2022
    Print publication:
    15 December 2022
  • During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.

Principles of Statistical Analysis
  • Learning from Randomized Experiments
  • Ery Arias-Castro
  • Published online:
    22 July 2022
    Print publication:
    25 August 2022
  • This compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance – simulation and sampling, as well as experimental design and data collection – that are typically displaced from introductory accounts. The core of the book then covers both standard methods and such advanced topics as multiple testing, meta-analysis, and causal inference.

Statistical Hypothesis Testing in Context
  • Reproducibility, Inference, and Science
  • Volume 52
  • Michael P. Fay, Erica H. Brittain
  • Published online:
    17 April 2022
    Print publication:
    05 May 2022
  • Fay and Brittain present statistical hypothesis testing and compatible confidence intervals, focusing on application and proper interpretation. The emphasis is on equipping applied statisticians with enough tools - and advice on choosing among them - to find reasonable methods for almost any problem and enough theory to tackle new problems by modifying existing methods. After covering the basic mathematical theory and scientific principles, tests and confidence intervals are developed for specific types of data. Essential methods for applications are covered, such as general procedures for creating tests (e.g., likelihood ratio, bootstrap, permutation, testing from models), adjustments for multiple testing, clustering, stratification, causality, censoring, missing data, group sequential tests, and non-inferiority tests. New methods developed by the authors are included throughout, such as melded confidence intervals for comparing two samples and confidence intervals associated with Wilcoxon-Mann-Whitney tests and Kaplan-Meier estimates. Examples, exercises, and the R package asht support practical use.

Computer Age Statistical Inference, Student Edition
  • Algorithms, Evidence, and Data Science
  • Bradley Efron, Trevor Hastie
  • Published online:
    26 October 2021
    Print publication:
    17 June 2021
  • The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? How does it all fit together? Now in paperback and fortified with exercises, this book delivers a concentrated course in modern statistical thinking. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov Chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. Each chapter ends with class-tested exercises, and the book concludes with speculation on the future direction of statistics and data science.

Mathematical Foundations of Infinite-Dimensional Statistical Models
  • Evarist Giné, Richard Nickl
  • Published online:
    05 March 2021
    Print publication:
    25 March 2021
  • In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.

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