Statistical Inference and the Plethora of Probability Paradigms: A Principled Pluralism

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability

Meta-critical thinking, paradox, and probabilities

There is as much lack of clarity concerning what “critical thinking” involves, even among those charged with teaching it, as there is consensus that we need more emphasis on it in both academia and society. There is an apparent need to think critically about critical thinking, an exercise that might be called meta-critical thinking. It involves emphasizing a practice in terms of which “critical thinking” is helpfully carried out and clarifying one or more of the concepts in terms of which “critical thinking” is usually defined. The practice is distinction making and the concept that of evidence. Science advances by constructing models that explain real-world processes. Once multiple potential models have been distinguished, there remains the task of identifying which models match the real-world process better than others. Since statistical inference has in large part to do with showing how data provide support, i.e., furnish evidence, that the model/hypothesis is more or less likely while still uncertain, we turn to it to help make the concept more precise and thereby useful. In fact, two of the leading methodological paradigms—Bayesian and likelihood—can be taken to provide answers to the questions of the extent to which as well as how data provide evidence for conclusions. Examining these answers in some detail is a highly promising way to make progress. We do so by way of the analysis of three well-known statistical paradoxes—the Lottery, the Old Evidence, and Humphreys’—and the identification of distinctions on the basis of which their plausible resolutions depend. These distinctions, among others between belief and evidence and different concepts of probability, in turn have more general applications. They are applied here to two highly contested public policy issues—the efficacy of COVID vaccinations and the fossil fuel cause of climate change. Our aim is to provide some tools, they might be called “healthy habits of mind,” with which to assess statistical arguments, in particular with respect to the nature and extent of the evidence they furnish, and to illustrate their use in well-defined ways

Temporal trends of triclosan contamination in dated sediment cores from four urbanized estuaries: Evidence of preservation and accumulation

Triclosan is an antimicrobial agent added to a wide array of consumer goods and personal care products. Through its use, it is introduced into municipal sewer systems where it is only partially removed during wastewater treatment. In this study, triclosan was measured in dated sediment cores from four urbanized estuaries in order to reconstruct temporal and spatial trends of accumulation. Measurable concentrations of triclosan first appeared in each of the sediment cores near 1964, which corresponds with the US patent issuance date of triclosan. The presence of triclosan at each of the study sites at or near the patent date indicates that long-term preservation is occurring in estuarine sediments. Temporal trends of triclosan at each location are unique, reflecting between site variability. Concentrations at one site climbed to as high as 400 ng g-1, due in part, to local commercial production of triclosan. At two locations, levels of triclosan rise towards the surface of each core, suggesting increasing usage in recent years. One location adjacent to a major combined sewer overflow had high sediment concentrations of triclosan, confirming their potential as a source of triclosan to estuaries