Evidential Statistics in Model and Theory Development

Samuel M Scheiner,Robert D Holt

doi:10.3389/fevo.2019.00306

Samuel M Scheiner, Robert D Holt

Open Access

https://doi.org/10.3389/fevo.2019.00306

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Abstract

Evidential statistics is an important advance in model and theory testing, and scientific reasoning in general, combining and extending key insights from other philosophies of statistics. A key desiderata in evidential statistics is the rigorous and objective comparison of alternative models against data. Scientific theories help to define the range of models which are brought to bear in any such assessment, including both tried and trusted models and risky novel models; such theories emerge from a kind of evolutionary process of repeated model assessment, where model selection is akin to natural selection acting both on the standing crop of genetic variation, and on novel mutations. The careful use of evidential statistics could play an important and as yet to be fulfilled role in the future development of scientific theories. We illustrate these ideas using examples from ecology and evolutionary biology.

Highlights

Statistical inference aims at relating models to data and the empirical world, whether that model deals with an issue as simple as estimating the mean of a population or as complex as predicting millennial-scale changes in the global climate
We have models of the movements of the continents over geological history, but those models are not mathematical equations
Evidential statistics is an important advance in model and theory testing, and scientific reasoning in general, combining and extending key insights from other philosophies of statistics

Summary

Introduction

Statistical inference aims at relating models to data and the empirical world, whether that model deals with an issue as simple as estimating the mean of a population or as complex as predicting millennial-scale changes in the global climate. There have been decades-long debates about the best way to make inferences (e.g., Neyman-Pearson error statistics vs Bayesian approaches) This special feature highlights the approach called “evidential statistics,” (Taper and Ponciano, 2016) which synthesizes prior approaches—error statistics, Bayesian statistics, information-based model selection, and likelihood approaches—to squarely focus on the comparative ability of alternative models or hypotheses for explaining an observed dataset. This approach to inference was sparked by Royall (1997) and Lele (2004), and the articles in this Special Issue highlight the rapid emergence and maturation of evidential statistics. We reflect on the need for intellectual flexibility by considering the role of statistical inference as a formal, mathematical procedure for refereeing the relationship between data, models, and theories, and place that in the context of the wider set of processes that scientists might use for theory development

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