Related papers: Probabilistic coherence and proper scoring rules
An informal and elementary introduction to probability scoring and forecast verification and improvement, slightly extended from Significance 22:3(2025)16, which might be useful for less mathematical readers as a prologue to the classic…
The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium…
Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most…
In this work we first illustrate the subjective theory of de Finetti. We recall the notion of coherence for both the betting scheme and the penalty criterion, by considering the unconditional and conditional cases. We show the equivalence…
Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze…
We prove a new version of Hall's Harem Theorem, where the final matching is realized by a unary function with additional conditions on behavior of cycles. The present paper can be considered as a helpful companion of the paper of the…
The stability rule for belief, advocated by Leitgeb [Annals of Pure and Applied Logic 164, 2013], is a rule for rational acceptance that captures categorical belief in terms of $\textit{probabilistically stable propositions}$: propositions…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness…
Consequences of the basic and most evident consistency requirement-that measured events cannot happen and not happen at the same time-are shortly reviewed. Particular emphasis is given to event forecast and event control. As a consequence,…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
This paper forges a strong connection between two seemingly unrelated forecasting problems: incentive-compatible forecast elicitation and forecast aggregation. Proper scoring rules are the well-known solution to the former problem. To each…
The aim of this paper is to prove characterization theorems for higher order derivations. Among others we prove that the system defining higher order derivations is stable. Further characterization theorems in the spirit of N.~G.~de Bruijn…
The probabilistic serial (PS) rule is a prominent randomized rule for assigning indivisible goods to agents. Although it is well known for its good fairness and welfare properties, it is not strategyproof. In view of this, we address…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
In this article I propose an approach for defining replicability for prediction rules. Motivated by a recent NAS report, I start from the perspective that replicability is obtaining consistent results across studies suitable to address the…
Conformal prediction is a statistically rigorous method for quantifying uncertainty in models by having them output sets of predictions, with larger sets indicating more uncertainty. However, prediction sets are not inherently actionable;…
We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be…