Related papers: Statistical inference as Green's functions

This paper introduces to readers the new concept and methodology of confidence distribution and the modern-day distributional inference in statistics. This discussion should be of interest to people who would like to go into the depth of…

As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g., rising costs, declining survey response rates), researchers increasingly use predictions from…

Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. The modeling is based on the probability density of measured variables expressed by experimental data via a kernel estimator. As…

We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…

In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant…

What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…

Outlying observations are frequently encountered across a wide spectrum of scientific domains, posing notable challenges to the generalizability of statistical models and the reproducibility of downstream analysis. They are identified…

We introduce inference methods for score decompositions, which partition scoring functions for predictive assessment into three interpretable components: miscalibration, discrimination, and uncertainty. Our estimation and inference relies…

As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…

In order to ensure the reliability of the explanations of machine learning models, it is crucial to establish their advantages and limits and in which case each of these methods outperform. However, the current understanding of when and how…

Selective inference is the problem of giving valid answers to statistical questions chosen in a data-driven manner. A standard solution to selective inference is simultaneous inference, which delivers valid answers to the set of all…

Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and…

We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…

As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…

We introduce a simple and intuitive framework that provides quantitative explanations of statistical models through the probabilistic assessment of input feature importance. The core idea comes from utilizing the Dirichlet distribution to…

Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…

The rapid advancement and widespread adoption of machine learning-driven technologies have underscored the practical and ethical need for creating interpretable artificial intelligence systems. Feature importance, a method that assigns…

We can, and should, do statistical inference on simulation models by adjusting the parameters in the simulation so that the values of {\em randomly chosen} functions of the simulation output match the values of those same functions…

For obtaining causal inferences that are objective, and therefore have the best chance of revealing scientific truths, carefully designed and executed randomized experiments are generally considered to be the gold standard. Observational…