Bayesian Analysis on a Noncentral Fisher–Student’s Hypersphere

Content Provider	Scilit
Author	Blanc, Richard Le
Copyright Year	2018
Description	Journal: The American Statistician Fisher succeeded early on in redefining Student's t-distribution in geometrical terms on a central hypersphere. Intriguingly, a noncentral analytical extension for this fundamental Fisher–Student's central hypersphere h-distribution does not exist. We therefore set to derive the noncentral h-distribution and use it to graphically illustrate the limitations of the Neyman–Pearson null hypothesis significance testing framework and the strengths of the Bayesian statistical hypothesis analysis framework on the hypersphere polar axis, a compact nontrivial one-dimensional parameter space. Using a geometrically meaningful maximal entropy prior, we requalify the apparent failure of an important psychological science reproducibility project. We proceed to show that the Bayes factor appropriately models the two-sample t-test p-value density of a gene expression profile produced by the high-throughput genomic-scale microarray technology, and provides a simple expression for a local false discovery rate addressing the multiple hypothesis testing problem brought about by such a technology.
Related Links	https://www.tandfonline.com/doi/pdf/10.1080/00031305.2017.1377111?needAccess=true
Ending Page	140
Page Count	15
Starting Page	126
ISSN	00031305
e-ISSN	15372731
DOI	10.1080/00031305.2017.1377111
Journal	The American Statistician
Issue Number	2
Volume Number	73
Language	English
Publisher	Informa UK Limited
Publisher Date	2019-04-03
Access Restriction	Open
Subject Keyword	Journal: The American Statistician Mathematical Social Sciences Confidence Intervals Bayesian Prior Bayesian Credible Intervals Multiple Hypothesis Testing Local False Discovery Rate
Content Type	Text
Subject	Statistics and Probability Statistics, Probability and Uncertainty