Related papers: A Bayesian Model of the Litigation Game
Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm,…
Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. In this paper we present methods for computing the probabilities of such…
Recently, topic modeling has been widely used to discover the abstract topics in text corpora. Most of the existing topic models are based on the assumption of three-layer hierarchical Bayesian structure, i.e. each document is modeled as a…
Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which…
We show that Bayes' rule provides an effective mechanism for creating document translation models that can be learned from only parallel sentences and monolingual documents---a compelling benefit as parallel documents are not always…
The paper studies one-shot two-player games with non-Bayesian uncertainty. The players have an attitude that ranges from optimism to pessimism in the face of uncertainty. Given the attitudes, each player forms a belief about the set of…
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…
In this paper, we study axiomatic foundations of Bayesian persuasion, where a principal (i.e., sender) delegates the task of choice making after informing a biased agent (i.e., receiver) about the payoff relevant uncertain state (see, e.g.,…
Decision-making under uncertainty and causal thinking are fundamental aspects of intelligent reasoning. Decision-making has been well studied when the available information is considered at the associative (probabilistic) level. The…
A core tension in models of concept learning is that the model must carefully balance the tractability of inference against the expressivity of the hypothesis class. Humans, however, can efficiently learn a broad range of concepts. We…
This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers…
There has been a recent media blitz on a cohort of mathematicians valiantly working to fix America's democratic system by combatting gerrymandering with geometry. While statistics commonly features in the courtroom (forensics, DNA analysis,…
Many multi-agent interaction scenarios can be naturally modeled as noncooperative games, where each agent's decisions depend on others' future actions. However, deploying game-theoretic planners for autonomous decision-making requires a…
In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
This paper addresses the question whether model knowledge can guide a defender to appropriate decisions, or not, when an attacker intrudes into control systems. The model-based defense scheme considered in this study, namely Bayesian…
There is a brief description of the probabilistic causal graph model for representing, reasoning with, and learning causal structure using Bayesian networks. It is then argued that this model is closely related to how humans reason with and…
Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations…
The systematic biases seen in people's probability judgments are typically taken as evidence that people do not reason about probability using the rules of probability theory, but instead use heuristics which sometimes yield reasonable…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…