Using statistical and computer models to quantify volcanic hazards

Technometrics

Volumn 51, Issue 4, 2009, Pages 402-413

  Bayarr, M J ^a   Berger, James O ^b   Calder, Eliza S ^c   Dalbey, Keith ^d   Lunagomez, Simon ^b   Patra, Abani K ^e   Pitman, E Bruce ^c   Spiller, Elaine T ^f   Wolpert, Robert L ^b  

^a UNIVERSITY OF VALENCIA   (Spain)

^b Duke University   (United States)

^c UNIVERSITY AT BUFFALO   (United States)

^d SANDIA NATIONAL LABORATORIES   (United States)

^e the State University of New York   (United States)

^f MARQUETTE UNIVERSITY   (United States)

Author keywords

Bayesian analysis; Catastrophic events; Emulators; Extreme events; Inverse problems

Indexed keywords

ADAPTIVE DESIGNS; BAYESIAN ANALYSIS; CATASTROPHIC EVENT; COMPUTER MODELING; COMPUTER MODELS; DIRECT SIMULATION; EMULATORS; EVENT PROBABILITY; EXTREME EVENTS; NATURAL HAZARD; PYROCLASTIC FLOWS; RARE EVENT; RARE EVENT SIMULATION; STATISTICAL MODELING; VOLCANIC FLOWS; VOLCANIC HAZARDS;

APPROXIMATION THEORY; BAYESIAN NETWORKS; DIFFERENTIAL EQUATIONS; HAZARDS; INVERSE PROBLEMS; PROBABILITY DENSITY FUNCTION; RISK ASSESSMENT; RISK MANAGEMENT; VOLCANOES;

SIMULATORS;

EID: 70549096874     PISSN: 00401706     EISSN: None     Source Type: Journal    
DOI: 10.1198/TECH.2009.08018     Document Type: Article

References (34)

1. Bayarri, M. J., Berger, J. O., Paulo, R., Sacks, J., Cafeo, J. A., Cavendish, J. C., Lin, C.-H., and Tu, J. (2007), "A Framework for Validation of Computer Models, " Technometrics, 49, 138-154.
2. Berger, J. O., and Bernardo, J. M. (1992), "On the Development of the Reference Prior Method, " in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Oxford, U.K.: Oxford University Press, pp. 35-49.
3. Bernardo, J. M., and Smith, A. F. M. (1994), Bayesian Theory. Wiley Series in Probability and Statistics, Chichester, U.K.: Wiley.
4. Booker, A. J., Dennis Jr., J. E., Frank, P. D., Serafini, D. B., Torczon, V., and Trosset, M.W. (1999), "A Rigorous Framework for Optimization of Expensive Functions by Surrogates, " Structural Optimization, 17, 1-13.
5. Calder, E. S., Cole, P. D., Dade, W. B., Druitt, T. H., Hoblitt, R. P., Huppert, H. E., Ritchie, L. J., Sparks, R. S. J., and Young, S. R. (1999), "Mobility of Pyroclastic Flows and Surges at the Soufrière Hills Volcano, Montserrat, " Geophysical Research Letters, 26, 537-540.
6. Calder, E. S., Luckett, R., Sparks, S. J., and Voight, B. (2002), "Mechanisms of Lava Dome Instability and Generation of Rockfalls and Pyroclastic Flows at Soufrière Hills Volcano, Montserrat, " in The Eruption of Soufrière Hills Volcano, Montserrat From 1995 to 1999. Geological Society Memoirs, Vol. 21, eds. T. H. Druitt and B. P. Kokelaar, London, U.K.: London Geological Society, pp. 173-190.
7. Coles, S. G. (2001), An Introduction to Statistical Modeling of Extreme Values, New York: Springer-Verlag.
8. Collins, G. S., and Melosh, H. J. (2003), "Acoustic Fluidization and the Extraordinary Mobility of Sturzstroms, " Journal of Geophysical Research, 108, 2473.
9. Currin, C., Mitchell, T. J., Morris, M. D., and Ylvisaker, D. (1991), "Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments, " Journal of the American Statistical Association, 86, 953-963.
10. Dade, W. B., and Huppert, H. E. (1998), "Long-Runout Rockfalls, " Geology, 26, 803-806.
11. Dalbey, K., Patra, A. K., Pitman, E. B., Bursik, M. I., and Sheridan, M. F. (2008), "Input Uncertainty Propagation Methods and Hazard Mapping of Geophysical Mass Flows, " Journal of Geophysical Research, 113, 1-16.
12. DuMouchel, W. H. (1983), "Estimating the Stable Index α in Order to Measure Tail Thickness, " The Annals of Statistics, 11, 1019-1036.
13. Fisher, R. A., and Tippett, L. H. C. (1928), "Limiting Forms of the Frequency Distributions of the Largest or Smallest Member of a Sample, " Mathematical Proceedings of Cambridge Philosophical Society, 24, 180-190.
14. Gramacy, R. B., Lee, H. K. H., and MacReady, W. G. (2004), "Parameter Space Exploration With Gaussian Process Trees, " in ICML-2004: Proceedings of the 21st International Conference on Machine Learning, eds. R. Greiner and D. Schuurmans, New York: ACM Press, pp. 353-360.
15. Gumbel, E. J. (1958), Statistics of Extremes, New York: Columbia University Press.
16. Herd, R. A., Edmonds, M., and Bass, V. A. (2005), "Catastrophic Lava Dome Failure at Soufrière Hills Volcano, Montserrat, 12-13 July 2003, " Journal of Volcanology and Geothermal Research, 148, 234-252.
17. Iman, R. L., Johnson, M. E., andWatson Jr., C. C., (2005), "Uncertainty Analysis for Computer Model Projections of Hurricane Losses, " Risk Analysis, 25, 1299-1312.
18. Iverson, R. M. (1997), "The Physics of Debris Flows, " Reviews of Geophysics, 35, 245-296.
19. Jeffreys, H. (1961), Theory of Probability, Oxford, U.K.: Oxford University Press.
20. Koehler, J. R., and Owen, A. B. (1996), "Computer Experiments, " in Handbook of Statistics, Vol. 13, eds. S. Ghosh and C. R. Rao, Amsterdam: Elsevier Science, pp. 261-308.
21. Patra, A. K., Bauer, A. C., Nichita, C. C., Pitman, E. B., Sheridan, M. F., and Bursik, M. I. (2005), "Parallel Adaptive Numerical Simulation of Dry Avalanches Over Natural Terrain, " Journal of Volcanology and Geothermal Research, 139, 1-21.
22. Ranjan, P., Bingham, D. R., and Michailidis, G. (2008), "Sequential Experiment Design for Contour Estimation From Complex Computer Codes, " Technometrics, 50, 527-541.
23. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989), "Design and Analysis of Computer Experiments, " Statistical Science, 4, 409-435.
24. Santner, T. J., Williams, B. J., and Notz, W. (2003), The Design and Analysis of Computer Experiments. Springer Series in Statistics, New York: Springer- Verlag.
25. Savage, S. B., and Hutter, K. (1989), "The Motion of a Finite Mass of Granular Material Down a Rough Incline, " Journal of Fluid Mechanics, 199, 177- 215.
26. Sheridan, M. F., Stinton, A. J., Patra, A. K., Pitman, E. B., Bauer, A. C., and Nichita, C. C. (2005), "Evaluating TITAN2D Mass-Flow Model Using the 1963 Little Tahoma Peak Avalanches, Mount Rainier, Washington, " Journal of Volcanology and Geothermal Research, 139, 89-102.
27. Smith, R. L. (1987), "Estimating Tails of Probability Distributions, " The Annals of Statistics, 15, 1174-107.
28. Tang, B. (1993), "Orthogonal Array-Based Latin Hypercubes, " Journal of the American Statistical Association, 88, 1392-1397.
29. Todorovic̀, P., and Zelenhasic̀, E. (1970), "A Stochastic Model for Flood Analysis, " Water Resources Research, 6, 1641-1648.
30. Voight, B., Sparks, R. S. J., Miller, A. D., Stewart, R. C., Hoblitt, R. P., Clarke, A. B., Ewart, J., Aspinall, W. P., Baptie, B., Calder, E. S., Cole, P. D., Druitt, T. H., Hartford, C., Herd, R. A., Jackson, P., Lejeune, A.-M., Lockhart, A. B., Loughlin, S. C., Luckett, R., Lynch, L., Norton, G. E., Robertson, R., Watson, I. M., Watts, R. B., and Young, S. R. (1999), "Magma Flow Instability and Cyclic Activity at Soufrière Hills Volcano, Montserrat, British West Indies, " Science, 283, 1138-1142.
31. Welch, W. J. (2003), "GaSP (Gaussian Stochastic Process), " personal communication.
32. Williams, B. J., Santner, T. J., and Notz, W. I. (2000), "Sequential Design of Computer Experiments to Minimize Integrated Responsed Functions, " Statistica Sinica, 10, 1133-1152.
33. Wolpert, R. L., and Ickstadt, K. (2004), "Reflecting Uncertainty in Inverse Problems: A Bayesian Solution Using Lévy Processes, " Inverse Problems, 20, 1759-1771.
34. Wolpert, R. L., and Taqqu, M. S. (2005), "Fractional Ornstein-Uhlenbeck Lévy Processes and the Telecom Process: Upstairs and Downstairs, " Signal Processing, 85, 1523-1545.