On the joint optimization of model selection and coding

The following problem is often encountered in many applications involving lossless and lossy data compression: one has m models at hand, each of which gives rise to a compression algorithm, and one wants to use these m models (or algorithms) to encode a sequence x/sup n/=x/sub 1/... x/sub n/ as efficiently as possible; due to nonstationarity, the sequence x/sup n/ may be governed, at different time instants, by different unknown models, and the question is how to use these models to optimally encode x/sup n/. In this paper, this problem is addressed by considering the joint optimization of model selection and coding, and is linked to rate distortion theory.