Related papers: The Essential Histogram
In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations…
Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first…
We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear…
A range of charts with different strengths and weaknesses exists to support the visual analysis of univariate distributions, with a limited understanding of which charts best support which tasks and users, and how practitioners use charts.…
Idealized probability distributions, such as normal or other curves, lie at the root of confirmatory statistical tests. But how well do people understand these idealized curves? In practical terms, does the human visual system allow us to…
How to extract useful insights from data is always a challenge, especially if the data is multidimensional. Often, the data can be organized according to certain hierarchical structure that are stemmed either from data collection process or…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…
The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…
Confidence intervals are an established means of portraying uncertainty about an inferred parameter and can be generated through the use of confidence distributions. For a confidence distribution to be ideal, it must maintain frequentist…
We prove calibration guarantees for the popular histogram binning (also called uniform-mass binning) method of Zadrozny and Elkan [2001]. Histogram binning has displayed strong practical performance, but theoretical guarantees have only…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…
Estimation frameworks for statistical inference are preferred to hypothesis testing when quantifying uncertainty and precise estimation are more valuable than binary decisions about statistical significance. Study design for…
For medical volume visualization, one of the most important tasks is to reveal clinically relevant details from the 3D scan (CT, MRI ...), e.g. the coronary arteries, without obscuring them with less significant parts. These volume datasets…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
Cartograms are maps in which areas of geographic regions (countries, states) appear in proportion to some variable of interest (population, income). Cartograms are popular visualizations for geo-referenced data that have been used for over…
Weighted histograms in Monte Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiments with random events that have weights. In this paper, the bin contents of…
Learning the distribution of natural images is one of the hardest and most important problems in machine learning. The problem remains open, because the enormous complexity of the structures in natural images spans all length scales. We…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…