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Popular Misconceptions About Bayesian Inference: Introduction to a Series of Blog Posts

“By seeking and blundering we learn.”

– Johann Wolfgang von Goethe

Bayesian methods have never been more popular than they are today. In the field of statistics, Bayesian procedures are mainstream, and have been so for at least two decades. Applied fields such as psychology, medicine, economy, and biology are slow to catch up, but in general researchers now view Bayesian methods with sympathy rather than with suspicion (e.g., McGrayne 2011).

The ebb and flow of appreciation for Bayesian procedures can be explained by a single dominant factor: pragmatism. In the early days of statistics, the only Bayesian models that could be applied to data were necessarily simple – the more complex, more interesting, and more appropriate models escaped the mathematically demanding derivations that Bayes’ rule required. This meant that unwary researchers who accepted the Bayesian theoretical outlook effectively painted themselves into a corner as far as practical application was concerned. How convenient then that the Bayesian paradigm was “absolutely disproved” (Peirce 1901, as reprinted in Eisele 1985, p. 748); how reassuring that it would “break down at every point” (Venn 1888, p. 121); and how comforting that it was deemed “utterly unacceptable” (Popper 1959, p. 150).

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A Personal Impression of the ASA Symposium on Statistical Inference: A World Beyond p<.05

 

I (Alex Etz) recently attended the American Statistical Association’s “Symposium on Statistical Inference” (SSI) in Bethesda Maryland. In this post I will give you a summary of its contents and some of my personal highlights from the SSI.

The purpose of the SSI was to follow up on the historic ASA statement on p-values and statistical significance. The ASA statement on p-values  was written by a relatively small group of influential statisticians and lays out a series of principles regarding what they see as the current consensus about p-values. Notably, there were mainly “don’ts” in the ASA statement. For instance: “P-values do not measure the probability that the studied hypothesis is true, nor the probability that the data were produced by random chance alone”; “Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold”; “A p-value, or statistical significance, does not measure the size of an effect or the importance of a result” (emphasis mine).

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An Interactive App for Designing Informative Experiments

Bayesian inference offers the pragmatic researcher a series of perks (Wagenmakers, Morey, & Lee, 2016). For instance, Bayesian hypothesis tests can quantify support in favor of a null hypothesis, and they allow researchers to track evidence as data accumulate (e.g., Rouder, 2014).

However, Bayesian inference also confronts researchers with new challenges, for instance concerning the planning of experiments. Within the Bayesian paradigm, is there a procedure that resembles a frequentist power analysis? (yes, there is!)

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Redefine Statistical Significance Part X: Why the Point-Null Will Never Die

In our previous post, we discussed the paper “Abandon Statistical Significance”, which is a response to the paper “Redefine Statistical Significance” that has dominated the contents of this blog so far. The Abandoners include Andrew Gelman and Christian Robert, and on their own blogs they’ve each posted a reaction to our Bayesian Spectacles post. Below is a short response to their reaction to the discussion of the reply to the original paper. 🙂

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