Improved harmonic mean estimator for phylogenetic model evidence

Journal of Computational Biology

Volumn 19, Issue 4, 2012, Pages 418-438

  Arima, Serena ^a   Tardella, Luca ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Bayes factor; harmonic mean; importance sampling; marginal likelihood; phylogenetic models; thermodynamic integration

Indexed keywords

ARTICLE; BAYES THEOREM; BIOLOGICAL MODEL; COMPUTER SIMULATION; GENETICS; PHYLOGENY; PLANT; PROBABILITY; THERMODYNAMICS;

BAYES THEOREM; COMPUTER SIMULATION; MARKOV CHAINS; MODELS, GENETIC; PHYLOGENY; PLANTS; THERMODYNAMICS;

EID: 84859329829     PISSN: 10665277     EISSN: None     Source Type: Journal    
DOI: 10.1089/cmb.2010.0139     Document Type: Article

References (61)

1. Abdo, Z., Minin, V.N., Joyce, P., et al. 2005. Accounting for uncertainty in the tree topology has little effect on the decision-theoretic approach to model selection in phylogeny estimation. Mol. Biol. Evol. 22, 691-703. (Pubitemid 40299518)
2. Aitichinson, J. 1986. The Statistical Analysis of Compositional Data. Chapman & Hall, London.
3. Altekar, G., Dwarkadas, S., Huelsenbeck, J.P., et al. 2004. Parallel metropolis-coupled Markov Chain Monte Carlo for Bayesian phylogenetic inference. Bioinformatics 20, 407-415. (Pubitemid 38262773)
4. Arima, S. 2009. Bayesian tools for complex statistical models in genetics [Ph.D. dissertation]. Sapienza Universitá di Roma, Rome.
5. Bartolucci, F., Scaccia, L., and Mira, A. 2006. Efficient Bayes factor estimation from the reversible jump output. Biometrika 93, 41-52.
6. Calderhead, B., and Girolami, M. 2009. Estimating Bayes Factors via thermodynamic integration and population MCMC. Comput. Stat. Data Anal. 53, 4028-4045.
7. Cavalli-Sforza, L.L., and Edwards, A.W.F. 1967. Phylogenetic analysis: models and estimation procedures. Evolution 21, 550-570.
8. Chen, M.H. 1994. Importance-weighted marginal Bayesian posterior density estimation. J. Am. Stat. Assoc. 89, 818-824.
9. Chen, M.H., and Shao, Q.M. 1997. On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Stat. 25, 1563-1594.
10. Do, K.D., Muller, P., and Vannucci, M. 2006. Bayesian Inference for Gene Expression and Proteomics. Cambridge University Press, New York.
11. Fan, Y., Wu, R., Chen, M.H., et al. 2011. Choosing among partition models in Bayesian phylogenetics. Mol. Biol. Evol. 28, 523-532.
12. Felsenstein, J. 1981. Evolutionary trees from DNA sequences: a maximum likelihood approach. J. Mol. Evol. 17, 368-376. (Pubitemid 11016207)
13. Felsenstein, J. 2004. Inferring Phylogenies. Sinauer, Sunderland, MA.
14. Fitch, W.M., and Margoliash, E. 1967. Construction of phylogenetic trees. Science 155, 279-284.
15. Frenkel, D. 1986. Free-energy competition and first-order phase transition. In Ciccotti, G., and Hover, W.G. (eds.), Molecular-Dynamics Simulation of Statistical-Mechanical Systems. North Holland, Amsterdam.
16. Friel, N., and Pettitt, A.N. 2008. Marginal likelihood estimation via power posteriors. J. R. Stat. Soc. B Stat. Methodol. 70, 589-607.
17. Gelfand, A.E., and Dey, D.K. 1994. Bayesian model choice: asymptotics and exact calculations. J. R. Stat. Soc. B Methodological 56, 501-514.
18. Gelman, A., and Meng, X.L. 1998. Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Stat. Sci. 13, 163-185. (Pubitemid 128466008)
19. Gowri-Shankar, V., and Jow, H. 2006. PHASE: a software package for PHylogenetics And Sequence Evolution, 2.0. University of Manchester, Manchester, UK.
20. Gowri-Shankar, V. 2006. RNA phylogenetic inference with heterogeneous substitution models [Ph.D. dissertation]. University of Manchester, Manchester, UK.
21. Green, P. 1995. Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrika 82, 711-732.
22. Hudelot, C., Gowri-Shankar, V., Jow, H., et al. 2003. RNA-based phylogenetic methods: application to mammalian mitochondrial RNA sequences. Mol. Phylogenet. Evol. 28, 241-252. (Pubitemid 37435990)
23. Huelsenbeck, J.P., and Ronquist, F. 2001. Mrbayes: Bayesian inference of phylogenetic trees. Bioinformatics 17, 754-755. (Pubitemid 32851390)
24. Huelsenbeck, J.P., Larget, B., and Alfaro, E. 2004. Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo. Mol. Biol. Evol. 21, 1123-1133. (Pubitemid 38658220)
25. Jukes, T.H., and Cantor, C.R. 1969. Evolution of protein molecules, 21-123 In Munro, H.N. (ed.), Mammalian Protein Metabolism. Academic Press, New York.
26. Kass, R.E., and Raftery, A. 1995. Bayes factor. J. Am. Stat. Assoc. 90, 773-795.
27. Lanave, C., Preparata, G., and Serio, G. 1984. A new method for calculating evolutionary substitution rates. J. Mol. Evol. 20, 86-93. (Pubitemid 14116237)
28. Larget, B., and Simon, D.L. 1999. Markov Chain Monte Carlo algorithms for the Bayesian analysis of phylogenetic trees. Mol. Biol. Evol. 16, 750-759. (Pubitemid 29260829)
29. Larget, B., Miller, R.E., Huelsenbeck, J.P., et al. 2002. Potential applications and pitfalls of Bayesian inference of phylogeny. Syst. Biol. 51, 673-688. (Pubitemid 35294801)
30. Lartillot, N., and Philippe, H. 2006. Computing Bayes factors using thermodynamic integration. Syst. Biol. 55, 195-207. (Pubitemid 43355101)
31. Lartillot, N., Brinkmann, H., and Philippe, H. 2007. Suppression of long branch attraction artefacts in the animal phylogeny using site-heterogeneous model. BMC Evol. Biol. 7.
32. Lefebvre, G., Steele, R., and Vandal, A.C. 2010. A path sampling identity for computing the Kullback-Leibler and J divergences Comput. Stat. Data Anal. 54, 1719-1731.
33. Lewis, P.O., Holder, M.T., and Swofford, D.L. 2008. Phycas: software for phylogenetic analysis. Available at: http:// www.phycas.org/. Accessed January 10, 2012.
34. Li, S., Pearl, D., and Doss, H. 2000. Phylogenetic tree reconstruction using Markov Chain Monte Carlo. J. Am. Stat. Assoc. 95, 493-508.
35. Minin, V.N, Abdo, Z., Joyce, P., et al. 2003. Performance-based selection of likelihood models for phylogeny estimation. Syst. Biol. 52, 674-683. (Pubitemid 37365048)
36. Newton, M.A., and Raftery, A. 1994. Approximate Bayesian inference by the weighted likelihood bootstrap. J. R. Stat. Soc B 56, 3-48.
37. Normana, J.A., Ericsonc, G.P., Jonssond, K.A., et al. 2009. A multi-gene phylogeny reveals novel relationships for aberrant genera of AustraloPapuan core Corvoidea and polyphyly of the Pachycephalidae and Psophodidae (Aves: Passeriformes). Mol. Phylogenet. Evol. 52, 488-497.
38. Ogata, Y. 1989. A Monte Carlo method for high dimensional integration. Numer. Math. 55, 137-157.
39. Petris, G., and Tardella, L. 2003. A geometric approach to transdimensional Markov chain Monte Carlo. Can. J. Stat. 31, 469-482. (Pubitemid 38390119)
40. Petris, G., and Tardella, L. 2007. New perspectives for estimating normalizing constants via posterior simulation [Technical Report]. Sapienza Universitá di Roma, Rome.
41. Pol, D. 2004. Empirical problems of the hierarchical likelihood ratio test for model selection. Syst. Biol. 53, 949-962. (Pubitemid 40141317)
42. Posada, D., and Crandall, K.A. 2001. Selecting the best-fit model of nucleotide substitution. Syst. Biol. 50, 580-601.
43. Posada, D., and Buckely, T.R. 2004. Model selection and model averaging in phylogenetics: advantages of Akaike information criterion and Bayesian approach over likelihood ratio test. Syst. Biol. 53, 793-808. (Pubitemid 39568279)
44. R Development Core Team. 2008. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
45. Raftery, M.A., Newton, A., Satagopan, J.M. et al. 2007. Estimating the integrated likelihood via posterior simulation using the harmonic mean identity. Proc. 8th Valencia Int Mtg. Bayesian Stat. 8 1-45.
46. Robert, R.C., and Wraith, D. 2009. Computational methods for Bayesian model choice. arXiv:0907.5123.
47. Rodrigue, N., Philippe, H., and Lartillot, N. 2007. Exploring fast computational strategies for probabilistic phylogenetic analysis. Syst. Biol. 55, 137-157.
48. Ronquist, F., and Huelsenbeck, J.P. 2003. MrBayes 3: Bayesian phylogenetic inference under mixed models. Bioinformatics 19, 1572:1574.
49. Ronquist, F., and Deans, A.R. 2010. Bayesian phylogenetics and its influence on insect systematics. Annu. Rev. Entomol. 55, 189-206.
50. Schwartz, G. 1978. Estimating the dimension of a model. Ann. Stat. 6, 461-464.
51. Sinsheimer, J.S., Lake, J.A., and Little, J.A. 1996. Bayesian hypothesis testing of four-taxon topologies using molecular sequence data. Biometrics 52, 193-210. (Pubitemid 26125103)
52. Swafford, D.L. 2003. PAUP: Phylogenetic Analysis Using Parsimony (and Other Methods). Sinauer Associates, Sunderland, MA.
53. Tiao, G.G., and Cuttman, I. 1965. The inverted Dirichlet distribution with applications. J. Am. Stat. Assoc. 311, 793-805.
54. Verdinelli, I., and Wasserman, L. 1995. Computing Bayes factor using a generalization of the Savage-Dickey density ratio. J. Am. Stat. Assoc. 90, 614-618.
55. von Reumont, B., Meusemann, K., Szucsich, N.U., et al. 2009. Can comprehensive background knowledge be incorporated into substitution models to improve phylogenetic analyses? A case study on major arthropod relationships. BMC Evol. Biol. 9, 1-19.
56. Wang, Z., Johnston, P.R., Yang, Z.L. et al. 2009. Evolution of reproductive morphology in leaf endophytes. PLoS ONE, 4, e4246.
57. Weiss, R.E., Suchard, M.A., and Sinsheimer, J.S. 2001. Bayesian selection of continuous-time Markov chain evolutionary models. Mol. Biol. Evol. 18, 1001-1013. (Pubitemid 32520473)
58. Xie, W., Lewis, P., Fan, Y., et al. 2011.. Improving marginal likelihood estimation for Bayesian phylogenetic model selection. Syst. Biol. 60, 150-160.
59. Yamanoue, Y., Miya, M., Matsuura, K., et al. 2008. A new perspective on phylogeny and evolution of tetraodontiform fishes (Pisces: Acanthopterygii) based on whole mitochondrial genome sequences: basal ecological diversification? SBMC Evol. Biol. 8, 212-226.
60. Yang, Z. 2006. Computational Molecular Evolution. OSEE, Oxford, UK.
61. Yang, Z. 2007. PAML 4: phylogentic analysis by maximum likelihood. Mol. Biol. Evol. 24, 1586-1591. (Pubitemid 47236688)