Subjectivity, Bayesianism, and Causality
This work addresses the foundational issue of subjectivity and causality in Bayesian reasoning, which is incremental by enriching existing frameworks rather than introducing a new paradigm.
The paper tackles the problem of modeling agency within Bayesian probability theory by proposing an abstract model of the subject that incorporates causal interventions, using a game-theoretic approach to formalize this in a measure-theoretic framework, and demonstrates its expressiveness with an example of causal induction.
Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by drawing parallels between Lacanian theory and Bayesian probability theory, and concludes that the latter must be enriched with causal interventions to model agency. The central contribution of this work is an abstract model of the subject that accommodates causal interventions in a measure-theoretic formalisation. This formalisation is obtained through a game-theoretic Ansatz based on modelling the inside and outside of the subject as an extensive-form game with imperfect information between two players. Finally, I illustrate the expressiveness of this model with an example of causal induction.