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Biometrika 2006 93(4):843-860; doi:10.1093/biomet/93.4.843
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© 2006 Biometrika Trust

Building mixture trees from binary sequence data

Shu-Chuan Chen1 and Bruce G. Lindsay2

1 Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287-1804, U.S.A. scchen{at}math.asu.edu, 2 Department of Statistics, Pennsylvania State University, University Park, Pennsylvania 16802-2111, U.S.A. bgl{at}psu.edu


  Abstract

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 DNA sequences of Griffiths & Tavaré (1994) shows that the approach performs well. Theoretical and computational properties of the ancestral mixture model are further developed.

Key Words: Ancestral mixture model; Evolutionary tree; Hierarchical tree; Sieve parameter.

Received October 2003. Revised May 2006.


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