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We examine the role of trustworthiness and trust in statistical inference, arguing that it is the extent of trustworthiness in inferential statistical tools which enables trust in the conclusions. Certain tools, such as the p-value and…
Neyman[106]'s seminal work in 1923 has been a milestone in statistics over the century, which has motivated many fundamental statistical concepts and methodology. In this review, we delve into Neyman[106]'s groundbreaking contribution and…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong…
An association rule is statistically significant, if it has a small probability to occur by chance. It is well-known that the traditional frequency-confidence framework does not produce statistically significant rules. It can both accept…
Machine and Statistical learning techniques become more and more important for the analysis of psychological data. Four core concepts of machine learning are the bias variance trade-off, cross-validation, regularization, and basis…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
Machine learning algorithms are increasingly deployed in critical domains such as finance, healthcare, and criminal justice [1]. The increasing popularity of algorithmic decision-making has stimulated interest in algorithmic fairness within…
The mathematical achievements of Harry Kesten since the mid-1950s have revolutionized probability theory as a subject in its own right and in its associations with aspects of algebra, analysis, geometry, and statistical physics. Through his…
We introduce the concept of an academic genealogy, or AG, and illustrate how AG charts may be constructed and then demonstrate how this methodology can be used by applying it to create the partial or full AG charts to two scientists, Paul…
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…
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…
Pearson's correlation coefficient is a popular statistical measure to summarize the strength of association between two continuous variables. It is usually interpreted via its square as percentage of variance of one variable predicted by…
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
Scientific datasets play a crucial role in contemporary data-driven research, as they allow for the progress of science by facilitating the discovery of new patterns and phenomena. This mounting demand for empirical research raises…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
Ever since the seminal work of R. A. Fisher and F. Yates, factorial designs have been an important experimental tool to simultaneously estimate the effects of multiple treatment factors. In factorial designs, the number of treatment…
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
Confounding seriously impairs our ability to learn about causal relations from observational data. Confounding can be defined as a statistical association between two variables due to inputs from a common source (the confounder). For…
Breiman challenged statisticians to think more broadly, to step into the unknown, model-free learning world, with him paving the way forward. Statistics community responded with slight optimism, some skepticism, and plenty of disbelief.…