Bayesian inference of the mean power of several Gaussian data

Giovanni Mana () and Carlo Palmisano ()
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Giovanni Mana: INRIM-Istituto Nazionale di Ricerca Metrologica
Carlo Palmisano: DMA-Diagnostic Monitoring Applications

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 6, 1-9

Abstract: Abstract 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. Graphical abstract

Date: 2024
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DOI: 10.1140/epjb/s10051-024-00737-w

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