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The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…

Other Statistics · Statistics 2013-01-15 Kalman Ziha

In this review, we recall the concepts of Identifiability and Observability of dynamical systems, and analyse them in the framework of Mathematical Epidemiology. We show that, even for simple and well known models of the literature, these…

Dynamical Systems · Mathematics 2023-05-23 Nik Cunniffe , Frédéric Hamelin , Abderrahman Iggidr , Alain Rapaport , Gauthier Sallet

The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple…

Methodology · Statistics 2022-04-19 Baoluo Sun , Zhonghua Liu , Eric Tchetgen Tchetgen

We study how the problem of observables is fully resolved for background independent theories defined on finite graphs. We argue the correct analogue of coordinate independence is the invariance under changes of graph labels, a kind of…

General Relativity and Quantum Cosmology · Physics 2025-08-05 Emil Broukal , Andrea Di Biagio , Eugenio Bianchi , Marios Christodoulou

The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or…

Methodology · Statistics 2015-08-04 Francesca Greselin , Ricardas Zitikis

We provide an overview of results relating to estimation and weak-instrument-robust inference in instrumental variables regression. Methods are implemented in the ivmodels software package for Python, which we use to illustrate results.

Econometrics · Economics 2025-08-19 Malte Londschien

As the amount of economic and other data generated worldwide increases vastly, a challenge for future generations of econometricians will be to master efficient algorithms for inference in empirical models with large information sets. This…

Computation · Statistics 2020-04-27 Dimitris Korobilis , Davide Pettenuzzo

Quantiles, expectiles and extremiles can be seen as concepts defined via an optimization problem, where this optimization problem is driven by two important ingredients: the loss function as well as a distributional weight function. This…

Methodology · Statistics 2024-05-21 Dieter Debrauwer , Irène Gijbels , Klaus Herrmann

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…

Statistics Theory · Mathematics 2013-03-27 Alexandre Janon , Thierry Klein , Agnes Lagnoux-Renaudie , Maëlle Nodet , Clémentine Prieur

Instrumental variables are commonly used to estimate effects of a treatment afflicted by unmeasured confounding, and in practice instruments are often continuous (e.g., measures of distance, or treatment preference). However, available…

Methodology · Statistics 2018-07-05 Edward H. Kennedy , Scott A. Lorch , Dylan S. Small

In this study, we investigate estimation and inference on a low-dimensional causal parameter in the presence of high-dimensional controls in an instrumental variable quantile regression. Our proposed econometric procedure builds on the…

Econometrics · Economics 2021-02-23 Jau-er Chen , Chien-Hsun Huang , Jia-Jyun Tien

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

Methodology · Statistics 2010-02-11 Christian P. Robert , Jean-Michel Marin , Judith Rousseau

In this paper, we draw attention to a promising yet slightly underestimated measure of variability - the Gini coefficient. We describe two new ways of defining and interpreting this parameter. Using our new representations, we compute the…

Statistics Theory · Mathematics 2022-10-13 Marta Milewska , Remco van der Hofstad , Bert Zwart

I thank Thomas Richardson and James Robins for their discussion of my paper, and discuss the similarities and differences between their approach to causal modelling, based on single world intervention graphs, and my own decision-theoretic…

Other Statistics · Statistics 2023-10-03 A. Philip Dawid

The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…

History and Philosophy of Physics · Physics 2026-05-22 Álvaro Mozota Frauca

Instrumental variables (IVs) are often continuous, arising in diverse fields such as economics, epidemiology, and the social sciences. Existing approaches for continuous IVs typically impose strong parametric models or assume homogeneous…

Methodology · Statistics 2025-10-17 Mei Dong , Lin Liu , Dingke Tang , Geoffrey Liu , Wei Xu , Linbo Wang

Instrumental variables have been widely used to estimate the causal effect of a treatment on an outcome. Existing confidence intervals for causal effects based on instrumental variables assume that all of the putative instrumental variables…

Methodology · Statistics 2016-07-14 Hyunseung Kang , T. Tony Cai , Dylan S. Small

World models have emerged as a unifying paradigm for learning latent dynamics, simulating counterfactual futures, and supporting planning under uncertainty. In this paper, we argue that computational epidemiology is a natural and…

Machine Learning · Computer Science 2026-04-14 Zeeshan Memon , Yiqi Su , Christo Kurisummoottil Thomas , Walid Saad , Liang Zhao , Naren Ramakrishnan

Inference for causal effects can benefit from the availability of an instrumental variable (IV) which, by definition, is associated with the given exposure, but not with the outcome of interest other than through a causal exposure effect.…

Methodology · Statistics 2012-01-13 Stijn Vansteelandt , Jack Bowden , Manoochehr Babanezhad , Els Goetghebeur

Global monitoring statistics play an important role for developing efficient monitoring schemes for high-dimensional data streams. A number of global monitoring statistics have been proposed in the literature. However, most of them only…

Methodology · Statistics 2017-12-19 Jun Li