Discrete Choices: A Comprehensive Guide to Distributions and Inference for Categorical Data

Discrete Choices: A Comprehensive Guide to Distributions and Inference for Categorical Data provides a unified and modern treatment of probability, inference, and modeling for categorical and discrete data. Although categorical outcomes are ubiquitous across statistics, data science, economics, epidemiology, and the social sciences, existing resources often treat these topics in fragmented ways, separating probability theory, inference, diagnostics, and applications into distinct texts. This book addresses that gap by presenting a coherent framework that begins with probability foundations and sampling theory, develops classical and hierarchical discrete distributions, and advances to modern likelihood-based and Bayesian inference. Core topics include Bernoulli, Binomial, Multinomial, and Poisson models; compound distributions such as the Beta–Binomial and Dirichlet–Multinomial; resampling methods; model diagnostics; and principled model selection. Advanced chapters extend this framework to high-dimensional categorical data, compositional data, network and relational structures, causal inference with multi-valued treatments, and fairness and bias diagnostics in categorical prediction. Extensive case studies and interactive hands-on data labs illustrate real-world applications in health, the social sciences, marketing, and text analytics, emphasizing reproducible and applied workflows. Balancing theoretical rigor with practical relevance, Discrete Choices: A Comprehensive Guide to Distributions and Inference for Categorical Data is suitable both as a graduate-level textbook and as a professional reference for researchers and practitioners working with discrete data.