Related papers: The Principle of Redundant Reflection
We propose a principled framework for nonparametric empirical Bayes (EB) estimation, based on the idea that the prior should be consistent with the observed posterior and that Bayesian updating should be stable. Focusing on discretized…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
It is commonly-accepted wisdom that more information is better, and that information should never be ignored. Here we argue, using both a Bayesian and a non-Bayesian analysis, that in some situations you are better off ignoring information…
It is commonly-accepted wisdom that more information is better, and that information should never be ignored. Here we argue, using both a Bayesian and a non-Bayesian analysis, that in some situations you are better off ignoring information…
It has been observed people tend to have opinions that are far more internally consistent than it would be reasonable to expect. Here, we study how that observation might emerge from changing how agents trust the opinions of their peers in…
Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes…
In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are…
The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on a few parameters. Even…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…
Belief integration methods are often aimed at deriving a single and consistent knowledge base that retains as much as possible of the knowledge bases to integrate. The rationale behind this approach is the minimal change principle: the…
In the classic AGM belief revision theory, beliefs are static and do not change their own shape. For instance, if p is accepted by a rational agent, it will remain p to the agent. But such rarely happens to us. Often, when we accept some…
Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…
Our opinions, which things we like or dislike, depend on the opinions of those around us. Nowadays, we are influenced by the opinions of online strangers, expressed in comments and ratings on online platforms. Here, we perform novel…
Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…
This paper considers a problem of distributed hypothesis testing and social learning. Individual nodes in a network receive noisy local (private) observations whose distribution is parameterized by a discrete parameter (hypotheses). The…
Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and…
In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data…
A natural way to represent beliefs and the process of updating beliefs is presented by Bayesian probability theory, where belief of an agent a in P can be interpreted as a considering that P is more probable than not P. This paper attempts…
Large language models (LLMs) generate outputs by utilizing extensive context, which often includes redundant information from prompts, retrieved passages, and interaction history. In critical applications, it is vital to identify which…
This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction,…