It was proved in the previous paper (Watanabe, J Mach Learn Res, 11:3571–3591, (2010), [16]) that Bayes cross validation is asymptotically equivalent to the widely applicable information criterion (WAIC), even if the posterior distribution can not be approximated by any normal distribution. In the present paper, we prove that they are equivalent to each other according to the second order asymptot
![Higher Order Equivalence of Bayes Cross Validation and WAIC](https://cdn-ak-scissors.b.st-hatena.com/image/square/8b32d8bf67b9500f98b6ec0b7a8cf4a9dad04474/height=288;version=1;width=512/https%3A%2F%2Fstatic-content.springer.com%2Fcover%2Fbook%2F978-3-319-97798-0.jpg)