Related papers: Information Threshold, Bayesian Inference and Deci…
We consider the problem of aggregating pairwise comparisons to obtain a consensus ranking order over a collection of objects. We use the popular Bradley-Terry-Luce (BTL) model which allows us to probabilistically describe pairwise…
We provide a novel analysis of Wald's sequential probability ratio test based on information theoretic measures for symmetric thresholds, symmetric noise, and equally likely hypotheses under the assumption that the test exactly terminates…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
We study belief revision when information is represented by a set of probability distributions, or general information. General information extends the standard event notion while including qualitative information (A is more likely than B),…
This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…
Bayesian optimal experimental design (OED) provides a principled framework for selecting observations or experiments. We introduce new Bayesian design criteria based on the expected Wasserstein-$p$ distance between the prior and posterior…
The relationship between a screening tests' positive predictive value, $\rho$, and its target prevalence, $\phi$, is proportional - though not linear in all but a special case. In consequence, there is a point of local extrema of curvature…
Consider a statistical problem where a set of parameters are of interest to a researcher. Then multiple confidence intervals can be constructed to infer the set of parameters simultaneously. The constructed multiple confidence intervals are…
The widely applicable information criterion (WAIC) has been used as a model selection criterion for Bayesian statistics in recent years. It is an asymptotically unbiased estimator of the Kullback-Leibler divergence between a Bayesian…
Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that…
Abstract In Extreme Value methodology the choice of threshold plays an important role in efficient modelling of observations exceeding the threshold. The threshold must be chosen high enough to ensure an unbiased extreme value index but…
Bayesian clinical trials can benefit of available historical information through the elicitation of informative prior distributions. Concerns are however often raised about the potential for prior-data conflict and the impact of Bayes test…
Observations on the past provide some hints about what will happen in the future, and this can be quantified using information theory. The ``predictive information'' defined in this way has connections to measures of complexity that have…
Two data-dependent information metrics are developed to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors from Berger, Bernardo, and…
Bayesian evidence ratios give a very attractive way of comparing models, and being able to quote the odds on a particular model seems a very clear motivation for making a choice. Jeffreys' scale of evidence is often used in the…
The use of Bayesian information criterion (BIC) in the model selection procedure is under the assumption that the observations are independent and identically distributed (i.i.d.). However, in practice, we do not always have i.i.d. samples.…
Informally, "Information Inconsistency" is the property that has been observed in many Bayesian hypothesis testing and model selection procedures whereby the Bayesian conclusion does not become definitive when the data seems to become…
A/B testing is ubiquitous within the machine learning and data science operations of internet companies. Generically, the idea is to perform a statistical test of the hypothesis that a new feature is better than the existing platform---for…
The Bayesian measure of sample information about the parameter, known as Lindley's measure, is widely used in various problems such as developing prior distributions, models for the likelihood functions and optimal designs. The predictive…
The following problem is considered: given a joint distribution $P_{XY}$ and an event $E$, bound $P_{XY}(E)$ in terms of $P_XP_Y(E)$ (where $P_XP_Y$ is the product of the marginals of $P_{XY}$) and a measure of dependence of $X$ and $Y$.…