Bayesian mixture modelling in geochronology via Markov chain Monte Carlo

Mathematical Geology

Volumn 38, Issue 3, 2006, Pages 269-300

  Jasra, Ajay ^a   Stephens, David A ^a   Gallagher, Kerry ^a   Holmes, Christopher C ^b,c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c MRC MAMMALIAN GENETICS UNIT   (United Kingdom)

Author keywords

Bayesian statistics; Geochronology; Mixture modelling; Reversible jump Markov chain Monte Carlo

Indexed keywords

GEOCHRONOLOGY; LEAD; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROBABILITY DISTRIBUTIONS; STATISTICAL METHODS; URANIUM; ZIRCON;

BASIN ANALYSIS; BAYESIAN ANALYSIS; DATA SET; ERROR ANALYSIS; GEOCHRONOLOGY; MARKOV CHAIN; MONTE CARLO ANALYSIS; NUMERICAL MODEL; PROBABILITY; URANIUM-LEAD DATING;

ASIA; AUSTRALASIA; AUSTRALIA; EURASIA; SOUTHEAST ASIA; THAILAND;

EID: 33745871916     PISSN: 08828121     EISSN: 15738868     Source Type: Journal    
DOI: 10.1007/s11004-005-9019-3     Document Type: Article

References (28)

1. Andersen, T., 2005, Detrital zircons as tracers of sedimentary provenance: Limiting conditions from statistics and numerical simulation: Chem. Geol., v. 216, p. 249-270.
2. Besag, J., 1986, On the statistical analysis of dirty pictures: J. R. Stat. Soc. B, v. 48, no. 3, p. 259-279.
3. Brandon, M. T., 1992, Decomposition of fission-track age distributions: Am. J. Sci. v. 292, p. 535-564.
4. Brandon, M. T., 1996, Probability density plot for fission-track grain-age samples: Rad. Meas., v. 26, no. 5, p. 663-676.
5. Brooks, S. P., Friel, N., and King, R., 2003, Classical model selection via simulated annealing: J. R. Stat. Soc. B, v. 65, no. 2, p. 503-520.
6. Carter, A., and Bristow, C. S., 2003, Linking hinterland evolution and continental basin sedimentation by using detrital zircon thermochronology: A study of the Khorat Plateau basin, Eastern Thailand: Basin Res., v. 15, no. 2, p. 271-285.
7. Carter, A., and Moss, S. J., 1999, Combined detrital-zircon fission track and U-Pb dating: A new approach to understanding hinterland evolution: Geology, v. 27, no. 3, p. 235-238.
8. Galbraith, R. F., 1998, Graphical display of estimates having differing standard errors: Technometrics, v. 30, p. 271-281.
9. Galbraith, R. F., 1998, The trouble with "probability density" plots of fission track ages: Radiat. Meas., v. 29, no. 2., p. 125-131.
10. Galbraith, R. F., and Green, P. F., 1990, Estimating the component ages in a finite mixture: Nucl. Track Radiat. Meas., v. 1, no. 3, p. 197-206.
11. Green, P. J., 1995, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination: Biometrika, v. 82, no. 4, p. 711-732.
12. Green, P. J., and Mira, A., 2001, Delayed rejection in reversible jump Metropolis-Hastings: Biometrika, v. 88, no. 4, p. 1035-1053.
13. Ireland, T. R., Flöttmann, T., Fanning, C. M., Gibson, G. M., and Preiss, W. V., 1998, Development of the early Paleozoic Pacific margin of Gondwana from detrital-zircon ages across the delamerian orogen: Geology, v. 26, no. 3, p. 243-246.
14. Ireland, T. R., and Williams, I. S. 2003, Considerations in zircon geochronology by SIMS, in Hanchar, J. M., and Hoskin, P. W. O., eds., Zircon: Reviews in mineralogy and geochemistry: Mineralogical Society of America, Washington, DC, vol. 53, p. 215-241.
15. Jasra, A., Holmes, C. C., and Stephens, D. A., 2005, Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modelling: Stat. Sci., v. 20, no. 1, p. 50-67.
16. Jennison, C., 1997, Discussion of on Bayesian analysis of mixtures with an unknown number of components: J. R. Stat. Soc. B., v. 59, no. 4, p. 778-779.
17. Jones, M. C., and Faddy, M. J., 2003, A skew extension of the t-distribution, with applications: J. R. Stat. Soc. B., v. 65, no. 1, p. 159-174.
18. Lindley, D. V., 1957, A statistical paradox: Biometrika, v. 44, no. 1, p. 187-192.
19. McLachlan, G. J., and Peel, D., 2000, Finite mixture models: Wiley, Chichester, UK, 419 p.
20. Richardson, S., and Green, P. J., 1997, On Bayesian analysis of mixture models with an unknown number of components: J. R. Stat. Soc. B, v. 59, no. 4, p. 731-792.
21. Richardson, S., Leblond, L., Jaussent, I., and Green, P. J., 2002, Mixture models in measurement error problems, with reference to epidemiological studies: J. R. Stat. Soc. A, v. 165, no. 3, p. 549-566.
22. Robert, C. P., 2001, The Bayesian choice: From decision-theoretic foundations to computational implementation, 2nd ed.: Springer, New York, 604 p.
23. Robert, C. P., and Casella, G., 2004, Monte Carlo statistical methods, 2nd ed.: Springer, New York, 645 p.
24. Sambridge, M. S., and Compston, W., 1994, Mixture modelling of multi-component data sets with application to ion-probe zircon ages: Earth Planet. Sci. Lett., v. 128, no. 3, p. 373-390.
25. Sircombe, K. N., 2004, AGEDISPLAY: An EXCEL workbook to evaluate and display univariate geochronological data using binned frequency histograms and probability density distributions: Comp. Geosci., v. 30, p. 21-31.
26. Stephens, M., 2000, Dealing with label switching in mixture models: J. R. Stat. Soc. B, v. 62, no. 4, p. 795-809.
27. Stern, R. A., and Amelin, Y., 2003, Assessment of errors in SIMS zircon U-Pb geochronology using a natural zircon standard and NIST SRM 610 glass: Chem. Geol., v. 197, no. 1, p. 111-142.
28. Vermeesch, P., 2004. How many grains are needed for a provenance study?: Earth. Planet. Sci. Lett., v. 224. p. 441-451.