Inference for stereological extremes

Journal of the American Statistical Association

Volumn 102, Issue 477, 2007, Pages 84-92

  Bortot, P ^a   Coles, S G ^b   Sisson, S A ^c  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Approximate bayesian computation; Extreme value theory; Markov chain Monte Carlo; Simulated tempering; Steel inclusion; Stereology

Indexed keywords

EID: 33947261211     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214506000000988     Document Type: Article

References (23)

1. Anderson, C. W., and Coles, S. G. (2002), "The Largest Inclusions in a Piece of Steel." Extremes, 5, 237-252.
2. Anderson, C. W., Shi, G., Atkinson, H. V., and Sellars, C. M. (2000), "The Precision of Methods Using the Statistics of Extremes for the Estimation of the Maximum Size of Inclusions in Clean Steels," Acta Materialia, 48, 4235-4246.
3. Baddeley, A., and Jensen. E. B. V. (2004), Stereology for Statisticians, Boca Raton. FL: Chapman & Hall/CRC.
4. Beaumont, M. A., Zhang, W., and Balding, D. J. (2002). "Approximate Bayesian Computation in Population Genetics," Genetics, 162, 2025-2035.
5. Beretta, S., and Murakami, Y. (1998), "Statistical Analysis of Defects for Fatigue Strength Prediction and Quality Control of Materials." Fatigue and Fracture of Engineering Materials & Structures, 21, 1049-1065.
6. Brooks, S. P., Friel, N., and King, R. (2003), "Classical Model Selection via Simulated Annealing," Journal of the Royal Statistical Society, Ser. B, 65, 503-520.
7. Coles, S. (2001), An Introduction to Statistical Modeling of Extreme Values. London: Springer-Verlag.
8. Drees, H., and Reiss, R.-D. (1992), Tail Behavior in Wicksell's Corpuscle Problem, Dordrecht: Kluwer.
9. Geyer, C. J., and Thompson, E. A. (1995), "Annealing Markov Chain Monte Carlo With Applications to Ancestral Inference," Journal of the American Statistical Association, 90, 909-920.
10. Hiubinka, D. (2003), "Stereology of Extremes: Shape Factor of Spheroids." Extremes, 6, 5-24.
11. Hobolth, A. (2003), "The Spherical Deformation Model," Biostatistics. 4, 583-595.
12. Marjoram, P., Molitor, J., Plagnol, V., and Tavaré, S. (2003), "Markov Chain Monte Carlo Without Likelihoods," Proceedings of the National Academy of Science, 100, 15324-15328.
13. Murakami, Y. (1994), "Inclusion Rating by Statistics of Extreme Values and Its Application to Fatigue Strength Prediction and Quality Control of Materials," Journal of Research of the National Institute of Standards and Technology, 99, 345-351.
14. Plagnol, V., and Tavaré, S. (2004), "Approximate Bayesian Computation and MCMC," in Monte Carlo and Quasi-Monte Carlo Methods 2002, ed. H. Niederreiter, Heidelberg: Springer-Verlag, pp. 99-114.
15. Shi, G., Atkinson, H. V., Sellars, C. M., and Anderson, C. W. (1999a), "Application of the Generalized Pareto Distribution to the Estimation of the Size of the Maximum Inclusion in Steels" Acta Materialia, 47, 1455-1468.
16. _ (1999b), "Comparison of Extreme Value Statistics Methods for Predicting Maximum Inclusion Size in Clean Steels." Ironmaking and Steelmaking, 26, 239-246.
17. Stolovitzky, G., and Berne, B. (2000). "Catalytic Tempering: A Method for Sampling Rough Energy Landscapes by Monte Carlo," Proceedings of the National Academy of Sciences USA, 97, 11164-11169.
18. Takahashi, R., and Sibuya, M. (1996), "The Maximum Size of the Planar Sections of Random Spheres and Its Application to Metallurgy," Annals of the Institute of Statistical Mathematics, 48, 127-144.
19. _ (1998), "Prediction of the Maximum Size in Wicksell's Corpuscle Problem," Annals of the Institute of Statistical Mathematics, 50, 361-377.
20. _ (2002), "Metal Fatigue, Wicksell Transform and Extreme Values," Applied Stochastics Models in Business and Industry, 18, 301-312.
21. Tanaka, M. M., Francis, A. R., Luciani, F., and Sisson, S. A. (2006), "Using Approximate Bayesian Computation to Estimate Tuberculosis Transmission Parameters From Genotype Data," Genetics, 173, 1511-1520.
22. Wicksell, S. D. (1925), "The Corpuscle Problem: A Mathematical Study of a Biometrie Problem," Biometrika, 17, 84-99.
23. _ (1926), "The Corpuscle Problem, Second Memoir: Case of Ellipsoidal Corpuscles," Biometrika, 18, 152-172.