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Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…
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…
Classical confidence limits are compared to Bayesian error bounds by studying relevant examples. The performance of the two methods is investigated relative to the properties coherence, precision, bias, universality, simplicity. A proposal…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…
Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision…
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…
Sequential Bayesian experimental design typically assumes that the number of experiments is fixed before data collection begins. In practical campaigns, however, experimentation may need to terminate early because additional measurements…
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…
Neuroimaging research has predominantly drawn conclusions based on classical statistics, including null-hypothesis testing, t-tests, and ANOVA. Throughout recent years, statistical learning methods enjoy increasing popularity, including…
In two recent papers, I have proposed a description of decision analysis that differs from the Bayesian picture painted by Savage, Jeffrey and other classic authors. Response to this view has been either overly enthusiastic or unduly…
This document presents the statistical methods used to process low-level measurements in the presence of noise. These methods can be classical or Bayesian. The question is placed in the general framework of the problem of nuisance…
It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…
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,…
Traditional statistical theory assumes that the analysis to be performed on a given data set is selected independently of the data themselves. This assumption breaks downs when data are re-used across analyses and the analysis to be…
Sample size determination is crucial in experimental design, especially in traffic and transport research. Frequentist statistics require a fixed sample size determined by power analysis, which cannot be adjusted once the experiment starts.…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…
We provide a brief overview of both Bayes and classical model selection. We argue tentatively that model selection has at least two major goals, that of finding the correct model or predicting well, and that in general both these goals may…
Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do…
We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different H\"older Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is…