A new look at Akaike’s Bayesian information criterion for inverse ill-posed problems

Akaike's Bayesian information criterion (ABIC) has been widely used in geophysical inversion and beyond. However, little done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution measurements, whose maximization directly leads invention ABIC by Akaike. show that is statistically estimate variance measurements prior maximizing measurements. The determination regularization parameter on basis actually equivalent estimating relative weighting factor between for inverse problems. if noise level unknown, tends produce a substantially biased In particular, since mean generally unknown but arbitrarily treated as zero inversion, does not reasonable either.