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Bayesian, frequentist and fiducial (BFF) inferences are much more congruous than they have been perceived historically in the scientific community (cf., Reid and Cox 2015; Kass 2011; Efron 1998). Most practitioners are probably more…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

This paper presents a brief, semi-technical comparison of the essential features of the frequentist and Bayesian approaches to statistical inference, with several illustrative examples implemented in Python. The differences between…

This note is a discussion commenting on the paper by Ly et al. on "Harold Jeffreys's Default Bayes Factor Hypothesis Tests: Explanation, Extension, and Application in Psychology" and on the perceived shortcomings of the classical Bayesian…

The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test…

Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…

We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential…

In this short review I present my personal reflections on QBism. I have no intrinsic sympathy neither to QBism nor to subjective interpretation of probability in general. However, I have been following development of QBism from its very…

(This comment has been updated to respond to Wang and Blei's rejoinder [arXiv:1910.07320].) The premise of the deconfounder method proposed in "Blessings of Multiple Causes" by Wang and Blei [arXiv:1805.06826], namely that a variable that…

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…

This study examines the application of Bayesian approach in the context of clinical trials, emphasizing their increasing importance in contemporary biomedical research. While conventional frequentist approach provides a foundational basis…

Between the two dominant schools of thought in statistics, namely, Bayesian and classical/frequentist, a main difference is that the former is grounded in the mathematically rigorous theory of probability while the latter is not. In this…

This short note points out two of the incongruences that I find in the Loredo (2012) comments on Andreon (2012), i.e. on my chapter written for the book "Astrostatistical Challenges for the New Astronomy". First, I find illogic the Loredo…

Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…

This book chapter (written in French) is a review of the foundations of the Bayesian approach to statistical inference, relating to its historical roots and some philosophical arguments, as well as a short presentation of its practical…

We have developed a frequentist approach for model selection which determines the consistency between any cosmological model and the data using the distribution of likelihoods from the iterative smoothing method. Using this approach, we…