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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper re-visits the problem of deciding between two simple hypotheses,the setting considered by Neyman and Pearson in developing their fundamentallemma. It studies the decision process induced by the most powerful test andthe receiver operating characteristic function associated with this decisionprocess. It addresses the question of how to report the decision arising fromthe decision function. It also examines the P-functional (the P-valuestatistic) and its role in the decision-making process. The impetus of thiswork is the continuing criticisms of statistical decision-making proceduresthat use the P-functional and a level of significance (LoS) of 0.05. A pointmade is that if one is going to use the value of the P-functional, then itshould be used in an equivalent manner as the most powerful decision function,but if one wants to obtain from its value the degree of support for eitherhypotheses, then the value of its density under the alternative is the properquantity to use. Replicability of results are discussed. Knowledge updatingthrough Bayes theorem when given the decision or the value of the P-functionalis also discussed, and it is argued that sequential learning is a coherent wayof finding the truth. But the impact of publication bias is also demonstratedto be quite serious in the search for truth. It is argued that decision-makersare free to choose their own LoS, since the additional summary measures willautomatically take their LoS choices into consideration. Three approaches forchoosing an optimal LoS are discussed and a procedure for sample sizedetermination is described. Ideas are illustrated by concrete problems and bythe lady tea-tasting experiment of Fisher which ushered null hypothesissignificance testing. It is hoped that by considering this fundamental settingof simple hypotheses, a better understanding of more complex settings willensue.

The Search for Truth through Data: NP Decision Processes, ROC Functions, $P$-Functionals, Knowledge Updating and Sequential Learning