For model-based frequentist statistics, based on a parametric statistical model ${{\cal M}_\theta }$, the trustworthiness of the ensuing evidence depends crucially on the validity of the probabilistic assumptions comprising ${{\cal M}_\theta }$, the optimality of the inference procedures employed, and the adequateness of the sample size to learn from data by securing –. It is argued that the criticism of the postdata severity evaluation of testing results based on a small n by Rochefort-Maranda is meritless because it conflates [a] misuses (...) of testing with [b] genuine foundational problems. Interrogating this criticism reveals several misconceptions about trustworthy evidence and estimation-based effect sizes, which are uncritically embraced by the replication crisis literature. (shrink)

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

This paper discusses two senses in which a hypothesis may be said to unify evidence. One is the ability of the hypothesis to increase the mutual information of a set of evidence statements; the other is the ability of the hypothesis to explain commonalities in observed phenomena by positing a common origin for them. On Bayesian updating, it is only mutual information unification that contributes to the incremental support of a hypothesis by the evidence unified. This poses a challenge for (...) the view that explanation is a confirmatory virtue that contributes to such incremental support; its advocates must ground it in some relevant difference between humans and a Bayesian agent. (shrink)

Exploratory statistics represents the transformation of a realist theory of statistics held by early nineteenth-century astronomers into an empiricist theory of statistics held by biometricians at the turn of the twentieth century. This paper discusses four key ideas in empiricist thought that influenced the form exploratory statistics took: (1) Baconianism, (2) associationism, (3) the search for cognitive calculi, and (4) phenomenalism. Some limitations of and alternatives to exploratory statistics as a hypothesis-generating methodology are discussed.

Laplace once argued that if one could “comprehend all the forces by which nature is animated,” it would be possible to predict the future and explain the past. The advent of analysis of large-scale data sets has been accompanied by newfound concerns about “Laplace’s Demon” as it relates to certain fields of science as well as management, evaluation, and audit. I begin by asking how statistical data are constructed, illustrating the hermeneutic acts necessary to create a variable. These include attributing (...) a certain characteristic to a particular phenomenon, isolating the characteristic of interest, and assigning a value to it. In addition, a population must be identified and a sample must be “taken” from that population. Next, I examine how statistical analyses are conducted, examining the interpretive acts there as well. In each case, I show how big data add new challenges. I then show how statistics are incorporated into audits and evaluations, emphasizing how alternative interpretations are concealed in the audit process. I conclude by noting that these issues cannot be “resolved” as Laplace suggested. His Demon, already banished from physics, needs to be banished from other fields of science, management, audits, and evaluations as well. (shrink)

It is argued in this paper that although much attention has been paid to causal chains and common causes within the literature on probabilistic causality, a primary virtue of that approach is its ability to deal with cases of multiple causation. In doing so some ways are indicated in which contemporary sine qua non analyses of causation are too narrow (and ways in which probabilistic causality is not) and an argument by Reichenbach designed to provide a basis for the asymmetry (...) of causation is refined. The importance of referring causal claims to an abstract model is also emphasized. (shrink)