Probabilistic models of sequences play a central role in most machine translation, automated speech recognition, lossless compression, spell-checking, and gene identification applications to name but a few. Unfortunately, real-world sequence data often exhibit long range dependencies which can only be captured by computationally challenging, complex models. Sequence data arising from natural processes also often exhibit power-law properties, yet common sequence models do not capture such properties. The sequence memoizer is a new hierarchical Bayesian model for discrete sequence data that captures long range dependencies and power-law characteristics while remaining computationally attractive. Its utility as a language model and general purpose lossless compressor is demonstrated. 1.