A Class of Prior Distributions on Context Tree Models and an Efficient Algorithm of the Bayes Codes Assuming It

The CTW (context tree weighting) algorithm is an efficient universal coding algorithm on context tree models. The CTW algorithm has been interpreted as the non-predictive Bayes coding algorithm assuming a special prior distribution over context tree models. An efficient recursive calculation method using a gathering context tree in the CTW algorithm is well known. Although there exist efficient recursive algorithms for the Bayes codes assuming a special class of prior distributions, the basic property of the prior distribution class has been scarcely investigated. In this paper we show the exact definition of a prior distribution class on context tree models that has the similar property to the class of conjugate priors. We show the posterior distribution is also included in the same distribution class as the prior distribution class. So we can also construct an efficient algorithm of predictive Bayes codes on context tree models by using the prior distribution class. Lastly the asymptotic mean code length of the codes is investigated.