Michael G. Titelbaum presents a new Bayesian framework for modeling rational degrees of belief, called the Certainty-Loss Framework. Subjective Bayesianism is epistemologists' standard theory of how individuals should change their degrees of belief over time. But despite the theory's power, it is widely recognized to fail for situations agents face every day. Michael G. Titelbaum argues that these failures stem from a common source: the inability ofConditionalization (Bayesianism's traditional updating rule) to model claims' going from certainty at an earlier time to less-than-certainty later on. He presents the first systematic, comprehensive Bayesian framework to accurately represent rational requirements on agents who undergo certainty loss. Titelbaumcompares the framework he proposes to alternatives, then applies it to cases in epistemology, decision theory, the theory of identity, and the philosophy of quantum mechanics. This is the first unified Bayesian framework capable of accurately modeling rational requirements in cases involving memory loss and context-sensitivity. It has applications to such diverse topics as indifference principles, relations among epistemic peers, Everettian interpretations ofquantum mechanics, the Fine-Tuning Argument for the multiverse, and the controversial Sleeping Beauty problem. Titelbaum develops his ambitious project with rigor and philosophical subtlety: the book makes a major contribution to the literature on formal epistemology.