On Bijective Variants of the Burrows-Wheeler Transform

The sort transform (ST) is a modification of the Burrows-Wheeler transform (BWT). Both transformations map an arbitrary word of length n to a pair consisting of a word of length n and an index between 1 and n. The BWT sorts all rotation conjugates of the input word, whereas the ST of order k only uses the first k letters for sorting all such conjugates. If two conjugates start with the same prefix of length k, then the indices of the rotations are used for tie-breaking. Both transforms output the sequence of the last letters of the sorted list and the index of the input within the sorted list. In this paper, we discuss a bijective variant of the BWT (due to Scott), proving its correctness and relations to other results due to Gessel and Reutenauer (1993) and Crochemore, Desarmenien, and Perrin (2005). Further, we present a novel bijective variant of the ST.Comment: 15 pages, presented at the Prague Stringology Conference 2009 (PSC 2009

Ignorability for categorical data

We study the problem of ignorability in likelihood-based inference from incomplete categorical data. Two versions of the coarsened at random assumption (car) are distinguished, their compatibility with the parameter distinctness assumption is investigated and several conditions for ignorability that do not require an extra parameter distinctness assumption are established. It is shown that car assumptions have quite different implications depending on whether the underlying complete-data model is saturated or parametric. In the latter case, car assumptions can become inconsistent with observed data.Comment: Published at http://dx.doi.org/10.1214/009053605000000363 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org