Rejoinder

We would like to thank all the discussants for their contributions. Our pap er attempts only a first step towards a satisfactory linkage between comple xity theory and coding-based inference and these discussions will help to b laze the paths for future exploration, We also take this opportunity to rem ind the reader that, in our opinion, MDL and R IR IL agree on many, many po ints. While ne certainly disagree with Dr Rissanen and he with us on quite a few points, we certainly acknowledge that these disagreements would under standably appear both infrequent and minor from the perspective of someone who knew relatively little about MDL and MML.