The discussion centers on the challenges of assigning a priori probabilities (P(H)) to hypotheses in scientific inference, particularly in the context of predictive success and falsifiability. Participants express uncertainty about how to effectively assign these probabilities, noting that only a limited number of hypotheses are typically developed to the point of making testable predictions. The conversation highlights the distinction between P(H) and P(H | \mathcal{M}), where \mathcal{M} represents the underlying model that connects hypotheses to observations. There is a consensus that while prior probabilities should have a basis, this aspect is often not included in mathematical formulations. The role of the model in determining probabilities is emphasized, with discussions on how observations that do not fit the model indicate the need for adjustments to the model or the consideration of new hypotheses. The thread also touches on the implications of Bayesian reasoning in relation to mental health, referencing an external article on the subject.
