Abstract
The Bayesian estimates b of the standard deviation σ in a linear model—as needed for the evaluation of reliability—is well known to be proportional to the square root of the Bayesian estimate (s 2) b of the variance component σ2 by a proportionality factor\(a_b = s_b /\sqrt {(s^2 )} _b \) involving the ratio of Gamma functions. However, in analogy to the case of the respective unbiased estimates, the troublesome exact computation ofa b may be avoided by a simple approximation which turns out to be good enough for most applications even if the degree of freedom ν is rather small.
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Schaffrin, B. Approximating the Bayesian estimate of the standard deviation in a linear model. Bull. Geodesique 61, 276–280 (1987). https://doi.org/10.1007/BF02521232
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DOI: https://doi.org/10.1007/BF02521232