Take a Risk:林岳彦の研究メモ





改めてDICの元論文であるSpigelhalter et al. (2002)*1を読んでいたら、DIC概念の導入のところ(p603)で以下のようにハッキリ書いてありました*2

Thus, by analogy with classical results described above, we propose a deviance information criterion DIC, defined as a classical estimate of fit, plus twice the effective number of parameters, to give

DIC=D(\overline{\theta})+2p_{D} (36)
=\overline{D}+p_{D} (37)

by definition of pD (10): equation (37) shows that DIC can also be considered as a Bayesian measure of fit or adequacy, penalized by an additional complexity term pD. From the results of section 3.2, we immediately see that in models with negligible prior information DIC will be approximately equivalent to Akaike's criterion.

やっぱり導入のところでは"by analogy"なんですね。

あと、(36)式のようにパラメータ数のペナルティはやっぱり2倍されているわけですね*3 *4。さらに(37)式を見ると、「平均値のdeviance」を「devianceの平均値」に置き換えるところでペナルティが半分に見える*5ことになるようです*6

*1:Bayesian measures of model complexity and fit. J R Statist Soc B 64: 583-639


*3:"by analogy"により!


*5:2pD → pD