‘Plausibility and the Solution to the Behrens-Fisher Problem’

‘Plausibility and the Solution to the Behrens-Fisher Problem’ is a detective story that reveals the solution to a mathematical conundrum that has kept statisticians perplexed for over a century.

The problem concerns what we can say about the difference between the true mean values of two Normal distributions from the information available in small samples.  Despite many attempts by academia to find the answer, usually involving either Fisher’s notion of ‘fiducial probability’ or using Bayes’ Rule with a ‘prior’ distribution, until now the correct solution has not been found.

The book shows that the problem is about what is plausible rather than what is probable and that it cannot be solved by the usual approaches and methods of mathematical statistics.  While they are closely connected, plausibility is not the same as probability.  The meaning of plausibility cannot be defined or devised; it must be discovered.

The book brings a fresh perspective to one of the most daunting challenges in the field, revealing why all previous attempts have failed and presenting the only possible correct solution.  It is a must-read for mathematicians and provides useful insights for anyone interested in assessments and deductions from statistical data.

The Book is published by Woodbridge Publishers and is available from Amazon in Hardcover (ISBN 978-1-917184-58-8) and Paperback (978-1-917184-57-1) forms, and also as a downloadable eBook.

(Brian Darbyshire / Woodbridge Publisher, 2024)

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