A perfectly rational Sleeping Beauty is put to sleep on Sunday night, and intermittently awoken either on Monday only (if a fair coin shows Heads) or on both Monday and Tuesday (if the fair coin shows Tails). According to experimental conditions, she neither remembers previous awakenings nor knows about passage of time, but she is aware of experimental conditions. Her credence for the coin having come up Heads is at the center of a scientific (mostly philosophical) controversy: halfers insist it (...) should be 1/2, while thirders claim it should be 1/3. Winkler (2017) reviewed the literature, in terminology accessible to statisticians. This paper presents a comprehensive treatment of the probability side of the problem, from the perspective of a frequentist applied statistician. Perceived contradictions are resolved (in line with Groisman 2008) or traced back to violation of model assumptions. Modeling was at the heart of the confusion and is also at the heart of the solution. (shrink)

A group of philosophers led by the late John Pollock has applied a method of reasoning about probability, known as direct inference and governed by a constraint known as Reichenbach's principle, to argue in support of ‘thirdism’ concerning the Sleeping Beauty Problem. A subsequent debate has ensued about whether their argument constitutes a legitimate application of direct inference. Here I defend the argument against two extant objections charging illegitimacy. One objection can be overcome via a natural and plausible definition, given (...) here, of the binary relation ‘logically stronger than’ between two properties that can obtain even when the respective properties differ from one another in ‘arity’; given this definition, the Pollock group's argument conforms to Reichenbach's principle. Another objection prompts a certain refinement of Reichenbach's principle that is independently well-motivated. My defense of the Pollock group's argument has epistemological import beyond the Sleeping Beauty problem, because it both widens and sharpens the applicability of direct inference as a method for inferring single-case epistemic probabilities on the basis of general information of a probabilistic or statistical nature. (shrink)