Bayesian Data Analysis, Andrew Gelman, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin, 2013 (Chapman & Hall)DOI: 10.1201/b16018 - A classic and comprehensive textbook on Bayesian methods, covering the principles of probabilistic modeling, likelihoods, priors, and posterior inference in full detail.
Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer)DOI: 10.1007/978-0-387-45528-3 - Provides a thorough probabilistic approach to machine learning, detailing generative models, probabilistic graphical models, and the fundamental components of building statistical models.
Probabilistic Graphical Models: Principles and Techniques, Daphne Koller and Nir Friedman, 2009 (MIT Press) - The definitive textbook on probabilistic graphical models, explaining how to encode structural assumptions and conditional independencies in complex probabilistic models.