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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

Causal influence measures for machine learnt classifiers shed light on the reasons behind classification, and aid in identifying influential input features and revealing their biases. However, such analyses involve evaluating the classifier…

Machine Learning · Computer Science 2018-04-10 Shayak Sen , Piotr Mardziel , Anupam Datta , Matthew Fredrikson

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…

Other Statistics · Statistics 2022-02-08 Rose D Baker

This paper addresses the problem of measurement errors in causal inference and highlights several algebraic and graphical methods for eliminating systematic bias induced by such errors. In particulars, the paper discusses the control of…

Methodology · Statistics 2012-03-19 Judea Pearl

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

Machine Learning · Statistics 2018-11-05 S. P. Lyddon , S. G. Walker , C. C. Holmes

One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…

Machine Learning · Statistics 2014-11-03 Ricardo Silva , Robin Evans

Observational data is increasingly used as a means for making individual-level causal predictions and intervention recommendations. The foremost challenge of causal inference from observational data is hidden confounding, whose presence…

Machine Learning · Statistics 2018-10-30 Nathan Kallus , Aahlad Manas Puli , Uri Shalit

The standard approach to answering an identifiable causal-effect query (e.g., $P(Y|do(X)$) when given a causal diagram and observational data is to first generate an estimand, or probabilistic expression over the observable variables, which…

Artificial Intelligence · Computer Science 2024-08-28 Anna Raichev , Alexander Ihler , Jin Tian , Rina Dechter

Measuring treatment effects in observational studies is challenging because of confounding bias. Confounding occurs when a variable affects both the treatment and the outcome. Traditional methods such as propensity score matching estimate…

Methodology · Statistics 2021-12-23 Bevan I. Smith , Charles Chimedza

Familiar statistical tests and estimates are obtained by the direct observation of cases of interest: a clinical trial of a new drug, for instance, will compare the drug's effects on a relevant set of patients and controls. Sometimes,…

Methodology · Statistics 2010-12-09 Bradley Efron

The possibility of unmeasured confounding is one of the main limitations for causal inference from observational studies. There are different methods for (partially) empirically assessing the plausibility of unconfoundedness. However, most…

Methodology · Statistics 2025-10-28 Fernando Pires Hartwig , Kate Tilling , George Davey Smith

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Methodology · Statistics 2015-06-22 Jeffrey W. Miller , David B. Dunson

A major challenge in estimating treatment effects in observational studies is the reliance on untestable conditions such as the assumption of no unmeasured confounding. In this work, we propose an algorithm that can falsify the assumption…

Methodology · Statistics 2025-06-03 Rickard K. A. Karlsson , Jesse H. Krijthe

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…

Methodology · Statistics 2017-03-14 Fani Tsapeli , Peter Tino , Mirco Musolesi

Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to 'mine' variables of interest…

Econometrics · Economics 2020-12-22 Mochen Yang , Edward McFowland , Gordon Burtch , Gediminas Adomavicius

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…

Econometrics · Economics 2021-12-08 Koen Jochmans , Martin Weidner

We revisit empirical Bayes discrimination detection, focusing on uncertainty arising from both partial identification and sampling variability. While prior work has mostly focused on partial identification, we find that some empirical…

Econometrics · Economics 2025-08-19 Jiaying Gu , Nikolaos Ignatiadis , Azeem M. Shaikh

Experiments deliver credible treatment-effect estimates but, because they are costly, are often restricted to specific sites, small populations, or particular mechanisms. A common practice across several fields is therefore to combine…

Econometrics · Economics 2025-12-30 Aristotelis Epanomeritakis , Davide Viviano

Estimating personalized treatment effects from high-dimensional observational data is essential in situations where experimental designs are infeasible, unethical, or expensive. Existing approaches rely on fitting deep models on outcomes…

Machine Learning · Computer Science 2022-02-02 Andrew Jesson , Panagiotis Tigas , Joost van Amersfoort , Andreas Kirsch , Uri Shalit , Yarin Gal

While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications, model error with nontrivial biases is unavoidable. A practical example is the error in the radiative transfer model…

Methodology · Statistics 2016-11-17 John Harlim , Tyrus Berry