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A platform for research: civil engineering, architecture and urbanism
Approximating the Bayesian estimate of the standard deviation in a linear model
Abstract The Bayesian estimatesb 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 (s2)b of the variance component $ σ^{2} $ 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 ofab 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.
Approximating the Bayesian estimate of the standard deviation in a linear model
Abstract The Bayesian estimatesb 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 (s2)b of the variance component $ σ^{2} $ 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 ofab 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.
Approximating the Bayesian estimate of the standard deviation in a linear model
Schaffrin, Burkhard (author)
Bulletin géodésique ; 61
1987
Article (Journal)
English
Geodäsie , Geometrie , Geodynamik , Zeitschrift , Mathematik , Mineralogie
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