Mixing Time for a Markov Chain on Cladograms

Combinatorics Probability and Computing

Volumn 9, Issue 3, 2000, Pages 191-204

  Aldous, David J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034397615     PISSN: 09635483     EISSN: None     Source Type: Journal    
DOI: 10.1017/S096354830000417X     Document Type: Article

References (21)

1. Aldous, D. J. (1982) Some inequalities for reversible Markov chains. J. London Math. Soc. (2) 25 564-576.
2. Aldous, D. J. (1993) The continuum random tree III. Ann. Probab. 21 248-289.
3. Aldous, D. J. (1994) Recursive self-similarity for random trees, random triangulations and Brownian excursion. Ann. Probab. 22 527-545.
4. Aldous, D. J. and Diaconis, P. (1986) Shuffling cards and stopping times. Amer. Math. Monthly 93 333-348.
5. Aldous, D. J. and Fill, J. A. (2000) Reversible Markov Chains and Random Walks on Graphs. Book in preparation.
6. Barker, D. LVB 1.0: Reconstructing evolution with parsimony and simulated annealing. http://www.icmb.ed.ac.uk/sokal.html.
7. Bayer, D. and Diaconis, P. (1992) Trailing the dovetail shuffle to its lair. Ann. Appl. Probab. 2 294-313.
8. Charleston, M. A. Landscape characteristics of tree space. http://taxonomy.zoology.gla.ac.uk/~mac/landscape/landscape.html.
9. Diaconis, P. (1988) Group Representations in Probability and Statistics, Institute of Mathematical Statistics, Hayward CA.
10. Diaconis, P., Fill, J. and Pitman, J. (1992) Analysis of top in at random shuffles. Combinatorics, Probability and Computing 1 135-155.
11. Diaconis, P. and Holmes, S. (1998) Matchings and phylogenetic trees. Proc. Nat. Acad. Sci. 95 14600-14602.
12. Diaconis, P. and Stroock, D. (1991) Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Probab. 1 36-61.
13. Durrett, R. (1991) Probability: Theory and Examples, Wadsworth, Pacific Grove CA.
14. Eldredge, N. and Cracraft, J. (1980) Phylogenic Patterns and the Evolutionary Process, Columbia University Press, New York.
15. Gilks, W. R., Richardson, S. and Spiegelhalter, D. J., eds (1996) Markov Chain Monte Carlo in Practice, Chapman and Hall, London.
16. Holmes, Susan P. (1998) Phylogenies: An overview. In Statistics in Genetics (B. Halloran and S. Geisser, eds), Vol. 112 of IMA Volumes in Mathematics and its Applications, Springer, New York, pp. 81-118.
17. Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains, Van Nostrand.
18. Li, S., Pearl, D. K., and Doss, H. (1996) Phylogenetic tree construction using MCMC. Technical Report 583, Statistics, Ohio State Univ.
19. Mau, B., Newton, M. A. and Larget, B. (1999) Bayesian phylogenetic inference via Markov chain Monte Carlo methods. Biometrics 55 1-12.
20. Palacios, J. L. and Tetali, P. (1996) A note on expected hitting times for birth and death chains. Stat. Probab. Letters 30 119-125.
21. Rosenthal, J. S. (1995) Convergence rates for Markov chains. SIAM Review 37 387-405.