The paper introduces the context-tree weighting method, a sequential universal data compression procedure for binary tree sources. The method efficiently recursive weights coding distributions corresponding to all bounded memory tree sources, achieving a desirable coding distribution for unknown model and parameter sources. The computational and storage complexity is low and depends on the average sequence length. The authors derive an upper bound on the cumulative redundancy, which includes coding, parameter, and model redundancy terms. This bound holds for all source sequence lengths and is derived using standard techniques. The method is shown to be optimal in the sense that it achieves the Rissanen lower bound on redundancy. The paper also discusses the implementation of the method, including encoding and decoding procedures, and addresses complexity issues. Additionally, it explores other weightings and generalizations to nonbinary sources.The paper introduces the context-tree weighting method, a sequential universal data compression procedure for binary tree sources. The method efficiently recursive weights coding distributions corresponding to all bounded memory tree sources, achieving a desirable coding distribution for unknown model and parameter sources. The computational and storage complexity is low and depends on the average sequence length. The authors derive an upper bound on the cumulative redundancy, which includes coding, parameter, and model redundancy terms. This bound holds for all source sequence lengths and is derived using standard techniques. The method is shown to be optimal in the sense that it achieves the Rissanen lower bound on redundancy. The paper also discusses the implementation of the method, including encoding and decoding procedures, and addresses complexity issues. Additionally, it explores other weightings and generalizations to nonbinary sources.