[どんどん積雪]
いわゆるミニ大通公園．
昨晩は雪がふりつづけていたみたいだけど，
朝は晴．
気温マイナス 5 度ぐらい
(本日の最高気温は -1.4 度だった)．
これはまだヌルくて，
明日からしばらく，
さらにキビしい真冬日が続くとゆー予報．
D Sun, RK Tsutakawa and PL Speckman. 1999. Posterior distribution of hierarchical models using CAR(1) distribuitons. Biometrika 86: 341-350. http://biomet.oxfordjournals.org/content/86/2/341.short.まあ，要旨をみますと第 11 章であつかってる状況そのままというかんぢだが ……
We examine properties of the conditional autoregressive model, or CAR(1) model, which is commonly used to represent regional effects in Bayesian analysis of mortality rates. We consider a Bayesian hierarchical linear mixed model where the fiexed effcts have a vague prior such as a constant prior and the random effect follows a class of CAR(1) models including those whose joint prior distribution of the regional effects is improper. We give sufficient condtions for the existence of the posterior distribuiton of the fixed and random effects and variance components. We then prove the necessity of the conditions and give a one-way analysis of variance example where the posterior may or may not exist. Finally, we extend the result to the generalised linear mixed model, which includes as a special case the Poisson log-linear model commonly used in disease mapping.
