https://doi.org/10.1140/epjb/s10051-024-00737-w
Regular Article - Statistical and Nonlinear Physics
Bayesian inference of the mean power of several Gaussian data
1
INRIM-Istituto Nazionale di Ricerca Metrologica, Strada delle cacce 91, 10135, Turin, Italy
2
Dipartimento di Fisica, UNITO-Università di Torino, via Pietro Giuria 1, 10125, Turin, Italy
3
DMA-Diagnostic Monitoring Applications, Turin, Italy
Received:
13
March
2024
Accepted:
17
June
2024
Published online:
29
June
2024
The uniform prior probability density for the means of normal data leads to inconsistent Bayesian inference of their mean power and jeopardizes the possibility of selecting among different models that explain the data. We reinvestigated the problem avoiding delivering unrecognised information and looking at it in a novel way. Namely, to consider a finite power, we used a normal prior minimally diverging from the uniform one, hyperparameterised by the mean and variance, and left the data to choose the most supported parameters. We also obtained an extended James–Stein estimator averaging the hyper-parameters and avoiding empirical Bayes techniques.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-024-00737-w.
© The Author(s) 2024
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