Related papers: Consistent Beliefs without Common Prior
Inference from limited data requires a notion of measure on parameter space, most explicit in the Bayesian framework as a prior. Here we demonstrate that Jeffreys prior, the best-known uninformative choice, introduces enormous bias when…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
Cheng (2025) establishes that in a persuasion game where both the sender and the receiver have Maxmin Expected Utility (MEU) preferences, the sender never strictly benefits from using ambiguous communication strategies over standard…
In the gambling foundation of probability theory, rationality requires that a subject should always (never) find desirable all nonnegative (negative) gambles, because no matter the result of the experiment the subject never (always)…
Conformal prediction (CP) was developed to provide finite-sample probabilistic prediction guarantees. While CP algorithms are a relatively general-purpose approach to uncertainty quantification, with finite-sample guarantees, they lack…
A considerable body of work in AI has been concerned with aggregating measures of confirmatory and disconfirmatory evidence for a common set of propositions. Claiming classical probability to be inadequate or inappropriate, several…
In statistical practice, whether a Bayesian or frequentist approach is used in inference depends not only on the availability of prior information but also on the attitude taken toward partial prior information, with frequentists tending to…
We introduce a robust belief-based measure of complexity. The idea is that task A is deemed more complex than task B if the probability of solving A correctly is smaller than the probability of solving B correctly regardless of the reward.…
Employing a generalized definition of Pratt (1964) and Arrow's (1965, 1971) probability premium, we introduce a new concept of attitude towards probability. We illustrate in a problem of risk sharing that whether attitude towards…
We provide an epistemic analysis of arbitrary strategic games based on possibility correspondences. We first establish a generic result that links true common beliefs (and, respectively, common knowledge) of players' rationality defined by…
In this paper, we show that the presence of the Archimedean and the mixture-continuity properties of a binary relation, both empirically non-falsifiable in principle, foreclose the possibility of consistency (transitivity) without…
We study cautious reasoning in finite sequential games played by agents with perfect recall. Our contribution lies in formulating a definition of prudent rationalizability (Heifetz et al. 2021, BEJTE) as an iterative reduction procedure of…
Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…
We unify standard frameworks for approachability both in full or partial monitoring by defining a new abstract game, called the "purely informative game", where the outcome at each stage is the maximal information players can obtain,…
A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…
We prove that in a general zero-sum repeated game where the first player is more informed than the second player and controls the evolution of information on the state, the uniform value exists. This result extends previous results on…
We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…
We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…