Related papers: Common $p$-Belief with Plausibility Measures: Exte…
In Neyman's original formulation, a 1-alpha confidence interval procedure is justified by its long-run coverage properties, and a single realized interval is to be described only by the slogan that it either covers the parameter or it does…
Merging beliefs requires the plausibility of the sources of the information to be merged. They are typically assumed equally reliable in lack of hints indicating otherwise; yet, a recent line of research spun from the idea of deriving this…
We define a class of groups equipped with an invariant probability measure, which includes all compact groups and is closed under taking ultraproducts with the induced Loeb measure; in fact, this class also contains the ultraproducts all…
This paper proposes a unified theoretical model to identify and test a comprehensive set of probabilistic updating biases within a single framework. The model achieves separate identification by focusing on the updating of belief…
We experimentally investigate how confidence over multiple priors affects belief updating. Theory predicts that the average Bayesian posterior is unaffected by confidence over multiple priors if average priors are the same. We manipulate…
Motivated by the problem of accurately predicting gap times between successive blood donations, we present here a general class of Bayesian nonparametric models for clustering. These models allow for prediction of new recurrences,…
This paper studies preference aggregation under risk. In our model, each agent has an incomplete preference relation represented by a set of expected utility functions. The classical Pareto principle is silent on agreement involving…
The Goodman-Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain…
Under model misspecification, it is known that Bayesian posteriors often do not properly quantify uncertainty about true or pseudo-true parameters. Even more fundamentally, misspecification leads to a lack of reproducibility in the sense…
A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau (IEEE…
We propose a probabilistic model to aggregate the answers of respondents answering multiple-choice questions. The model does not assume that everyone has access to the same information, and so does not assume that the consensus answer is…
In the setting where information cannot be verified, we propose a simple yet powerful information theoretical framework---the Mutual Information Paradigm---for information elicitation mechanisms. Our framework pays every agent a measure of…
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$,…
Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…
The safe integration of machine learning modules in decision-making processes hinges on their ability to quantify uncertainty. A popular technique to achieve this goal is conformal prediction (CP), which transforms an arbitrary base…
A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…
We study processes of societal knowledge accumulation, where the validity of a new unit of knowledge depends both on the correctness of its derivation and on the validity of the units it depends on. A fundamental question in this setting…
When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models…
We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…