Related papers: Information Threshold, Bayesian Inference and Deci…
We study a repeated information design setting in which the receiver, who is also the decision-maker, updates beliefs in a systematically biased way. More specifically, a distorted posterior in our model can be written as a convex…
The mutual information between two jointly distributed random variables $X$ and $Y$ is a functional of the joint distribution $P_{XY},$ which is sometimes difficult to handle or estimate. A coarser description of the statistical behavior of…
We use the language of uninformative Bayesian prior choice to study the selection of appropriately simple effective models. We advocate for the prior which maximizes the mutual information between parameters and predictions, learning as…
Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…
A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization, we provide an approach to characterizing the amount of information a prior…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
Recently proposed methods in data subset selection, that is active learning and active sampling, use Fisher information, Hessians, similarity matrices based on gradients, and gradient lengths to estimate how informative data is for a…
This paper presents a decision-theoretic approach to statistical inference that satisfies the likelihood principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of…
This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states. These measures should have important appli- cations in…
There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…
Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds.…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…
DeGroot (1962) developed a general framework for constructing Bayesian measures of the expected information that an experiment will provide for estimation. We propose an analogous framework for measures of information for hypothesis…
Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given dataset. Privacy restrictions may require the curator of the data or the respondents themselves…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
Living in the 'Information Age' means that not only access to information has become easier but also that the distribution of information is more dynamic than ever. Through a large-scale online field experiment, we provide new empirical…
The principle of `information causality' can be used to derive an upper bound---known as the `Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. To date,…
In problems with large amounts of missing data one must model two distinct data generating processes: the outcome process which generates the response and the missing data mechanism which determines the data we observe. Under the…
We consider probabilistic theories in which the most elementary system, a two-dimensional system, contains one bit of information. The bit is assumed to be contained in any complete set of mutually complementary measurements. The…