Related papers: Frequentist statistics as a theory of inductive in…

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.…

There is much interest in providing probabilistic semantics for defaults but most approaches seem to suffer from one of two problems: either they require numbers, a problem defaults were intended to avoid, or they generate peculiar side…

One can argue that one of the main roles of the subject of statistics is to characterize what the evidence in collected data says about questions of scientific interest. There are two broad questions that we will refer to as the estimation…

A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…

Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental and practically relevant questions about probability and inference that puzzled our founding fathers remain unanswered. To…

Likelihood ratio tests are a widely used method in global analyses in particle physics. The computation of the statistical significance (p-value) of these tests is usually done with a simple formula that relies on Wilks' theorem. There are,…

\citet{Rosenbaum83ps} introduced the notion of the propensity score and discussed its central role in causal inference with observational studies. Their paper, however, caused a fundamental incoherence with an early paper by…

Deciding whether a model provides a good description of data is often based on a goodness-of-fit criterion summarized by a p-value. Although there is considerable confusion concerning the meaning of p-values, leading to their misuse, they…

Motivation: Combining the results of different experiments to exhibit complex patterns or to improve statistical power is a typical aim of data integration. The starting point of the statistical analysis often comes as sets of p-values…

This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…

Between Bayesian and frequentist inference, it's commonly believed that the former is for cases where one has a prior and the latter is for cases where one has no prior. But the prior/no-prior classification isn't exhaustive, and most…

Statistical inference from data is a foundational task in science. Recently, it has received growing attention for its central role in inference systems of primary interest in data sciences and machine learning. However, the understanding…

Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…

Bayesian and frequentist criteria fundamentally differ, but often posterior and sampling distributions agree asymptotically (e.g., Gaussian with same covariance). For the corresponding single-draw experiment, we characterize the frequentist…

Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…

Following a paper in which the fundamental aspects of probabilistic inference were introduced by means of a toy experiment, details of the analysis of simulated long sequences of extractions are shown here. In fact, the striking performance…

In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter…

There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…

Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…

Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…