D'Agostini's Bayesian gamma prior and Cowan's frequentist gamma variance model are the same gamma law under the parameter map k = lambda = (n-1)/2 = 1/(4 epsilon^2).
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Implementing Errors on Errors: Bayesian vs Frequentist
D'Agostini's Bayesian gamma prior and Cowan's frequentist gamma variance model are the same gamma law under the parameter map k = lambda = (n-1)/2 = 1/(4 epsilon^2).