Related papers: Revisiting Simpson's Paradox: a statistical misspe…
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…
The parametric g-formula is an approach to estimating causal effects of sustained treatment strategies from observational data. An often cited limitation of the parametric g-formula is the g-null paradox: a phenomenon in which model…
The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…
One of the fundamental challenges found throughout the data sciences is to explain why things happen in specific ways, or through which mechanisms a certain variable $X$ exerts influences over another variable $Y$. In statistics and machine…
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…
Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models.…
Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…
Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about…
Meta-analysis is an important tool for combining results from multiple studies and has been widely used in evidence-based medicine for several decades. This paper reports, for the first time, an interesting and valuable paradox in…
In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…
The paper argues that a part of the current statistical discussion is not based on the standard firm foundations of the field. Among the examples we consider are prediction into the future, semi-supervised classification, and causality…
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…
This paper discusses different needs and approaches to establishing ``causation'' that are relevant in legal cases involving statistical input based on epidemiological (or more generally observational or population-based) information. We…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…
We describe a simple probabilistic method to cross-identify astrophysical sources from different catalogs and provide the probability that a source is associated with a source from another catalog or that it has no counterpart. When the…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
How can we draw trustworthy scientific conclusions? One criterion is that a study can be replicated by independent teams. While replication is critically important, it is arguably insufficient. If a study is biased for some reason and other…
If we accept Savage's set of axioms, then all uncertainties must be treated like ordinary probability. Savage espoused subjective probability, allowing, for example, the probability of Donald Trump's re-election. But Savage's probability…
Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on…