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This paper examines the quantities used by MYCIN to reason with uncertainty, called certainty factors. It is shown that the original definition of certainty factors is inconsistent with the functions used in MYCIN to combine the quantities.…

How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? I propose we utilize the posterior distribution of a causal effect and present the probability of the effect being greater…

In this paper, we propose standard statistical tools as a solution to commonly highlighted problems in the explainability literature. Indeed, leveraging statistical estimators allows for a proper definition of explanations, enabling…

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…

The Jeffreys-Lindley paradox stands as the most profound divergence between frequentist and Bayesian approaches to hypothesis testing. Yet despite more than six decades of discussion, this paradox remains frequently misunderstood--even in…

Under model misspecification, it is known that Bayesian posteriors often do not properly quantify uncertainty about true or pseudo-true parameters. Even more fundamentally, misspecification leads to a lack of reproducibility in the sense…

Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…

The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…

In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its…

Quantum paradoxes show that quantum statistics can exceed the limits of positive joint probabilities for physical properties that cannot be measured jointly. It is therefore impossible to describe the relations between the different…

A fundamental task in science is to determine the underlying causal relations because it is the knowledge of this functional structure what leads to the correct interpretation of an effect given the apparent associations in the observed…

This paper investigates the use of synthetic control methods for causal inference in macroeconomic settings when dealing with possibly nonstationary data. While the synthetic control approach has gained popularity for estimating…

Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…

Statistical learning using imprecise probabilities is gaining more attention because it presents an alternative strategy for reducing irreplicable findings by freeing the user from the task of making up unwarranted high-resolution…

A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that…

Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices.…

In this paper, I will demonstrate a new perspective on the Two Envelope Problem. I hope to show with convincing clarity how the paradox results from an inherent problem pertaining to the interpretation of Bayesian probability. Specifically,…

To many statisticians and citizens, the outcome of the most recent U.S. presidential election represents a failure of data-driven methods on the grandest scale. This impression has led to much debate and discussion about how the election…

In the present paper, we investigate consequence relations that are both paraconsistent and plausible (but still monotonic). More precisely, we put the focus on pivotal consequence relations, i.e. those relations that can be defined by a…

Machine learning algorithms can produce biased outcome/prediction, typically, against minorities and under-represented sub-populations. Therefore, fairness is emerging as an important requirement for the large scale application of machine…