7 New Bayesian Inference Books Reshaping the Field in 2025

What sets this book apart is its rigorous yet accessible treatment of Bayesian inference, crafted by Silvelyn Zwanzig and Rauf Ahmad. Zwanzig's extensive background in mathematical statistics and Ahmad's expertise in high-dimensional inference converge to unpack theory, methods, and computational techniques with clarity. You will find formal theorems accompanied by detailed proofs, intuitive explanations, and a wealth of examples and exercises, including R code. This book is tailored for master's students and researchers aiming to deepen their grasp of exact Bayesian methods, with a dedicated chapter on computational techniques that bridges theory and practice. If you seek a solid foundation grounded in mathematical rigor, this book fits that need precisely.

This book challenges the usual parametric assumptions by delving into Jean-Marie Rolin's pioneering work on nonparametric Bayesian estimation. Compiled posthumously by Jean-Pierre Florens and Michel Mouchart, it brings together Rolin's unpublished papers that explore the mathematical foundations of Bayesian models, including concepts like sufficiency and invariance, alongside practical applications such as the Dirichlet process and Polya urn models. You gain insight into advanced statistical structures and their applications in fields like econometrics and biometrics, especially through Rolin's unique treatment of duration models. If you're seeking to deepen your grasp of Bayesian theory beyond textbook cases, this offers a rigorous, detail-rich resource, though it demands a solid statistical background to fully appreciate.

This tailored book explores the latest developments and discoveries in Bayesian inference as of 2025, focusing on cutting-edge techniques that shape the future of statistical analysis. It delves into contemporary advances such as nonparametric methods, objective Bayesian frameworks, and emerging applications in data science and social research. By aligning closely with your background and interests, this personalized resource hones in on the topics you find most relevant, helping you stay ahead of evolving methodologies and new insights. Through detailed examinations of recent research and innovative approaches, the book reveals how these breakthroughs expand Bayesian inference's reach and enhance analytical precision. The tailored content ensures you engage deeply with material that matches your specific goals and learning preferences, making complex subjects accessible and applicable to your unique pursuits.

The latest insights in this book come from Jose M Bernardo and Dongchu James O Berger, whose extensive experience in statistics shines through its pages. They challenge the common notion that Bayesian analysis is inherently subjective, tracing the history of objective Bayesian inference from the late 18th century to today. You gain a clear understanding of the reference prior approach, a method they advocate for its transparency and rigor, alongside a practical toolkit tailored for both statisticians and curious scientists. Whether you’re new to Bayesian methods or exploring its philosophical roots, this book equips you with concrete frameworks to analyze data intuitively and objectively.

Drawing from his extensive research at CONICET and his hands-on contributions to Python libraries like PyMC and ArviZ, Osvaldo Martin offers a deeply practical guide to Bayesian modeling. You explore probabilistic programming through modern tools, learning not only to build models but also to critically evaluate and refine them using real and synthetic data. For example, the chapters on hierarchical models and Bayesian additive regression trees reveal sophisticated methods made approachable. This book suits you well if you have Python experience and want to translate Bayesian theory into applied data science without wading through overly technical jargon.

What started as a need to demystify Bayesian methods for social scientists led Jeff Gill and Le Bao to craft this accessible guide. You gain a solid grasp of Bayesian probability and inference without requiring advanced math beyond basic statistics. The book bridges theory and practice, showing you how to implement models with real-world social science data using R and Python code. Chapters unfold with clear explanations and examples that build your intuition about Bayesian principles and their applications. This is ideal if you want a practical foundation in Bayesian analysis tailored to social science contexts.

This tailored book explores emerging Bayesian methods tailored to your interests and background, focusing on the latest discoveries shaping the field in 2025. It covers how new techniques and insights are transforming Bayesian inference, revealing advances in nonparametric approaches, objective frameworks, and probabilistic modeling that align with your specific goals. By concentrating on developments most relevant to your expertise, this book enables a focused and efficient learning experience. Designed to match your professional context, the content delves into cutting-edge research and applications, helping you stay ahead with a personalized exploration of Bayesian trends. This approach ensures you engage deeply with impactful topics without wading through extraneous material.

Drawing from decades of experience in social science research, David Kaplan offers a focused guide on applying Bayesian methodologies tailored to this field. You will gain a clear understanding of frequentist versus epistemic probability, along with practical skills using the RStan software for advanced statistical modeling. The book dives into modern topics like Hamiltonian Monte Carlo and Bayesian variable selection, enriched with examples from large educational databases such as PISA. If you’re working with social data and want to harness the latest Bayesian tools for model evaluation and uncertainty, this book provides detailed frameworks and annotated code to help you do just that.

After extensive research in statistics and biostatistics, Michael J. Daniels and his co-authors developed this book to address key challenges in causal inference and missing data using Bayesian nonparametric methods. You’ll explore how flexible Bayesian techniques help model complex data relationships while accommodating assumptions that are often untestable, such as missing at random and unconfoundedness. The book guides you through foundational concepts, advanced BNP tools, and practical case studies featuring health records and clinical trial data, offering you a concrete understanding of applying these methods to real-world problems. If you’re involved in statistical research or medical data analysis with a strong mathematical background, this book gives you nuanced insights into minimizing model misspecification risks.