Building mixture trees from binary sequence data

We develop a new method for building a hierarchical tree from binary sequence data. It is based on an ancestral mixture model. The sieve parameter in the model plays the role of time in the evolutionary tree of the sequences. By varying the sieve parameter, one can create a hierarchical tree that estimates the population structure at each fixed backward point in time. Application to the clustering of the mitochondrial  sequences of Griffiths & Tavaré (1994) shows that the approach performs well. Theoretical and computational properties of the ancestral mixture model are further developed.