We present an investigation of recently proposed character and word sequence kernels for the task of authorship attribution based on relatively short texts. Performance is compared with two corresponding probabilistic approaches based on Markov chains. Several configurations of the sequence kernels are studied on a relatively large dataset (50 authors), where each author covered several topics. Utilising Moffat smoothing, the two probabilistic approaches obtain similar performance, which in turn is comparable to that of character sequence kernels and is better than that of word sequence kernels. The results further suggest that when using a realistic setup that takes into account the case of texts which are not written by any hypothesised authors, the amount of training material has more influence on discrimination performance than the amount of test material. Moreover, we show that the recently proposed author unmasking approach is less useful when dealing with short texts.