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- W3139453755 abstract "Akaike's Bayesian information criterion (ABIC) has been widely used in geophysical inversion and beyond. However, little has been done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution of measurements, whose maximization directly leads to the invention of ABIC by Akaike. We show that ABIC is to statistically estimate the variance of measurements and the prior variance by maximizing the marginal distribution of measurements. The determination of the regularization parameter on the basis of ABIC is actually equivalent to estimating the relative weighting factor between the variance of measurements and the prior variance for geophysical inverse problems. We show that if the noise level of measurements is unknown, ABIC tends to produce a substantially biased estimate of the variance of measurements. In particular, since the prior mean is generally unknown but arbitrarily treated as zero in geophysical inversion, ABIC does not produce a reasonable estimate for the prior variance either." @default.
- W3139453755 created "2021-03-29" @default.
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- W3139453755 date "2021-05-01" @default.
- W3139453755 modified "2023-09-27" @default.
- W3139453755 title "A new look at Akaike’s Bayesian information criterion for inverse ill-posed problems" @default.
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- W3139453755 doi "https://doi.org/10.1016/j.jfranklin.2021.03.003" @default.
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