Related papers: A Bayesian View on the Dr. Evil Scenario
This article solves the Hume's problem of induction using a probabilistic approach. From the probabilistic perspective, the core task of induction is to estimate the probability of an event and judge the accuracy of the estimation.…
In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it…
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…
In this paper is presented a simple alternative model of the dual nature of light, based on the deliberate inversion of the original statement from P. A. M. Dirac: "Each photon interferes only with itself. Interference between different…
Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown…
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 this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
We propose an extension of Poole's independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of…
We investigate how distorted, yet structured, beliefs can persist in strategic situations. Specifically, we study two-player games in which each player is endowed with a biased-belief function that represents the discrepancy between a…
Many resources for forensic scholars and practitioners, such as journal articles, guidance documents, and textbooks, address how to make a value of evidence assessment in the form of a likelihood ratio (LR) when deciding between two…
We study several bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow to accurately compute the posterior distribution of the time…
In this paper, we consider the problem of social learning, where a group of agents embedded in a social network are interested in learning an underlying state of the world. Agents have incomplete, noisy, and heterogeneous sources of…
To make decisions we are guided by the evidence we collect, as well as the opinions of friends and neighbors. How do we integrate our private beliefs with information we obtain from our social network? To understand the strategies humans…
Significant controversy remains about what constitute correct self-locating beliefs in scenarios such as the Sleeping Beauty problem, with proponents on both the "halfer" and "thirder" sides. To attempt to settle the issue, one natural…
Recently many simple principles have been proposed that can explain quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments. However, few implications between these principles are…
One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent,…
No man is an island, as individuals interact and influence one another daily in our society. When social influence takes place in experiments on a population of interconnected individuals, the treatment on a unit may affect the outcomes of…
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…