Related papers: A Population's Feasible Posterior Beliefs

We consider the disclosure problem of a sender with a large data set of hard evidence who wants to persuade a receiver to take higher actions. Because the receiver will make inferences based on the distribution of the data they see, the…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

We introduce multi-population opinion dynamics models linked to the bounded confidence model, aiming to explore how interactions between individuals contribute to the emergence of consensus, polarization, or fragmentation. Existing models…

We examine information structures in settings with privately informed agents and an informationally constrained mediator who supplies additional public signals. Our focus is on characterizing the set of posteriors that the mediator can…

An important use of machine learning is to learn what people value. What posts or photos should a user be shown? Which jobs or activities would a person find rewarding? In each case, observations of people's past choices can inform our…

Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…

We study a Bayesian persuasion setting in which a sender wants to persuade a critical mass of receivers by revealing partial information about the state to them. The homogeneous binary-action receivers are located on a communication…

Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t-test. In contrast, the Bayesian versions of the t-test have languished in obscurity. In recent years, however, the theoretical and practical…

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge.…

The ideal Bayesian agent reasons from a global probability model, but real agents are restricted to simplified models which they know to be adequate only in restricted circumstances. Very little formal theory has been developed to help…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

Interest in how democracies form consensus has increased recently, with statistical physics and economics approaches both suggesting that there is convergence to a fixed point in belief networks, but with fluctuations in opinions when there…

Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop…

This paper studies a general class of social choice problems in which agents' payoff functions (or types) are privately observable random variables, and monetary transfers are not available. We consider cardinal social choice functions…

Bayesian persuasion studies how an informed sender should partially disclose information so as to influence the behavior of self-interested receivers. In the last years, a growing attention has been devoted to relaxing the assumption that…

In the present paper a model of a market consisting of real and financial interacting sectors is studied. Agents populating the stock market are assumed to be not able to observe the true underlying fundamental, and their beliefs are biased…

This note introduces the concept of a partially specified prior distribution for certain post hoc inference problems, where a finite population is sampled once in order to make a decision on the presence or complete absence of some…

The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

A multi-level model of opinion formation is presented which takes into account that attitudes on different issues are usually not independent. In the model, agents exchange beliefs regarding a series of facts. A cognitive structure of…

We state the problem of inverse reinforcement learning in terms of preference elicitation, resulting in a principled (Bayesian) statistical formulation. This generalises previous work on Bayesian inverse reinforcement learning and allows us…