English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

• the frequentist framework is unable to distinguish between relevant and irrelevant multiplicity adjustments; from the frequentist perspective all possible collections of tests seem equally valid to adjust for. • the Bayesian framework, by using posterior probabilities as a basis for inference, offers a clear and coherent distinction. Within this framework it is relevant to adjust for those tests that are associated with the test under consideration. Here, we defined two tests to be associated if either the hypotheses, or the data sets, of the tests are associated. Within the Bayesian framework, the association between hypotheses is encoded by joint prior distributions on these. We have shown that this formality of the Bayesian framework helps to reason about the set of relevant adjustments in the light of background context, which we expressed by means of directed acyclic graphs. We noted, however, that it may be hard to specify joint prior distributions, and that the set of relevant adjustments may be extremely large. Thus, for practical purposes we proposed a compromise, where the formal statistical analysis is done within the standard frequentist framework (e.g. by computing p values or confidence intervals), and the adjustment for multiplicity is done informally, by reasoning qualitatively about the association of hypotheses. In particular, we have recommended surveying the available evidence and making it available as part of the ‘Discussion’ section of applied epidemiological papers. One step further would be to borrow information across tests or comparisons. In that sense, we view GH’s favored hierarchical modeling approach as being in line with (and a further formalization of) our recommendations. Our reasoning on directed acyclic graphs has further led us to draw two conclusions that may not seem immediately intuitive. First: when testing two hypotheses on related data set, the Bayesian framework generally requires adjustment of the first test for the second test, even if the two hypotheses are unrelated. This is so because the test statistic of the first hypothesis is a collider between the first hypothesis and the test statistic of the second test. Second: when doing a fishing expedition on unrelated hypotheses and data sets, there is no need to make any multiplicity adjustment within the Bayesian framework, since the posterior for any of the hypothesis does not, in this case, depend on the test statistics of the other tests or on the selection mechanism induced by the data fishing. We would like to emphasize that this is only so provided that a correct Bayesian analysis is considered, and that standard frequentist measures (e.g. p values) are not necessarily justified under an (informal) frequentist analysis. * Arvid Sjölander arvid.sjolander@ki.se

Authors’ reply to ‘Multiple comparisons controversies are about context and costs, not frequentism versus Bayesianism’