INFORMATION CHANGE THE WORLD

International Journal of Mathematical Sciences and Computing(IJMSC)

ISSN: 2310-9025 (Print), ISSN: 2310-9033 (Online)

Published By: MECS Press

IJMSC Vol.6, No.2, Apr. 2020

Bayesian Parameter Inference of Explosive Yields Using Markov Chain Monte Carlo Techniques

Full Text (PDF, 657KB), PP.1-17


Views:3   Downloads:1

Author(s)

John Burkhardt

Index Terms

Bayesian inference, nonlinear regression, explosive yield, Markov chain Monte Carlo.

Abstract

A Bayesian parameter inference problem is conducted to estimate the explosive yield of the first atomic explosion at Trinity in New Mexico. The first of its kind, the study advances understanding of fireball dynamics and provides an improved method for the determination of explosive yield. Using fireball radius-time data taken from archival film footage of the explosion and a physical model for the expansion characteristics of the resulting fireball, a yield estimate is made. Bayesian results from the Markov chain indicate that the estimated parameters are consistent with previous calculation except for the critical parameter that modifies the independent time variable. This unique result finds that this parameter deviates in a statistically significant way from previous predictions. Use of the Bayesian parameter estimates computed is found to greatly improve the ability of the fireball model to predict the observed data. In addition, parameter correlations are computed from the Markov chain and discussed. As a result, the method used increases basic understanding of fireball dynamics and provides an improved method for the determination of explosive yields.


Cite This Paper

John Burkhardt." Bayesian Parameter Inference of Explosive Yields Using Markov Chain Monte Carlo Techniques", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.6, No.2, pp.1-17, 2020. DOI: 10.5815/ijmsc.2020.02.01

Reference

[1] Mack JE. U.S. Atomic Energy Commission. Semi-popular motion-picture record of the Trinity explosion. Oak Ridge, TN: Atomic Energy Commission; 1946.

[2] Taylor GI. The Formation of a Blast Wave by a Very Intense Explosion. I. Theoretical Discussion Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 1950; 201:159-174.

[3] Taylor GI. The Formation of a Blast Wave by a Very Intense Explosion. II. The Atomic Explosion of 1945 Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 1950; 201:175-186.

[4] Bethe HA and Fuchs K. Measurement of Nuclear Bomb Efficiency by Observation of the Ball of Fire at Early Stages Los Alamos Scientific Laboratory, Tech. Rep. LA-516; 1946.

[5] Gallant AR. Nonlinear regression. The American Statistician 1975; 29:73-81.

[6] Kass RE. Nonlinear regression analysis and its applications. Journal of the American Statistical Association 1990; 85:594-596.

[7] Casella G., and Berger R. Statistical inference. Belmont, CA: Brooks/Cole Cengage Learning; 2017.

[8] Boos D., and Stefanski L. Essential statistical inference: Theory and methods (Springer texts in statistics, v. 120). Dordrecht: Springer; 2012.

[9] Wasserman L. All of statistics: A concise course in statistical inference (Corrected second print. ed., Springer texts in statistics). New York: Springer; 2010.

[10] Fahrmeir L. Kneib T, Lang S, and Marx,B. Regression. Berlin: Springer-Verlag; 2007.

[11] Wakefield J. Bayesian and frequentist regression methods (Springer series in statistics). New York: Springer; 2013.

[12] Seber G.A, and Wild CJ. Nonlinear regression analysis. New York: John Wiley and Sons; 1989.

[13] Bernardo JM, and Smith AF. Bayesian theory. New York: John Wiley and Sons; 2009.

[14] Gelman,A, Carlin JB, Stern HS, and Rubin DB. Bayesian data analysis. Chapman and Hall/CRC; 2013.

[15] Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, and Teller E. Equation of state calculations by fast computing machines. The Journal of Chemical Physics 1953; 21, 1087.

[16] Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 1970; 57:97-109.

[17] Box GE, and Tiao GC. Bayesian inference in statistical analysis (Vol. 40). New York: John Wiley & Sons; 2011.

[18] Denison DG, Holmes CC., Mallick BK., and Smith AF. Bayesian methods for nonlinear classification and regression (Vol. 386). New York: John Wiley and Sons; 2002.

[19] Porzel FB, Rate of Growth of Atomic Fireballs Los Alamos Scientific Laboratory, Tech. Rep. LA-1214, Unclassified, Distribution Unlimited; 1951.