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Title: Bayesian MCMC estimation of the rose of directions (English)
Author: Prokešová, Michaela
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 39
Issue: 6
Year: 2003
Pages: [703]-717
Summary lang: English
Category: math
Summary: The paper concerns estimation of the rose of directions of a stationary fibre process in $R^3$ from the intersection counts of the process with test planes. A new approach is suggested based on Bayesian statistical techniques. The method is derived from the special case of a Poisson line process however the estimator is shown to be consistent generally. Markov chain Monte Carlo (MCMC) algorithms are used for the approximation of the posterior distribution. Uniform ergodicity of the algorithms used is shown. Properties of the estimation method are studied both theoretically and by simulation. (English)
Keyword: rose of directions
Keyword: planar section
Keyword: fibre process
Keyword: Bayesian statistics
Keyword: MCMC algorithm
MSC: 62F15
MSC: 62M09
MSC: 62M30
MSC: 62M99
MSC: 65B05
MSC: 65C40
idZBL: Zbl 1248.62039
idMR: MR2035645
Date available: 2009-09-24T19:58:06Z
Last updated: 2015-03-24
Stable URL:
Reference: [1] Beneš V., Gokhale A. M.: Planar anisotropy revisited.Kybernetika 36 (2000), 149–164 MR 1760022
Reference: [2] Campi S., Haas, D., Weil W.: Approximaton of zonoids by zonotopes in fixed directions.Discrete Comput. Geom. 11 (1994), 419–431 MR 1273226, 10.1007/BF02574016
Reference: [3] Cruz-Orive L. M., Hoppeler H., Mathieu, O., Weibel E. R.: Stereological analysis of anisotropic structures using directional statistics.Appl. Statist. 34 (1985), 14–32 Zbl 0571.62045, MR 0793336, 10.2307/2347881
Reference: [4] Hilliard J. E.: Specification and measurement of microstructural anisotropy.Trans. Metall. Soc. AIME 224 (1962), 1201–1211
Reference: [5] Geyer C. J.: Practical Markov chain Monte Carlo (with discussion).Statist. Sci. 7 (1992), 473–511 10.1214/ss/1177011137
Reference: [6] Hlawiczková M., Ponížil, P., Saxl I.: Estimating 3D fibre process anisotropy.In: Topics in Applied and Theoretical Mathematics and Computer Science (V. V. Kluev and N. E. Mastorakis), WSEAS Press, WSEAS, 2001, 214–219 Zbl 1039.60009, MR 2029416
Reference: [7] Kiderlen M.: Non-parametric estimation of the directional distribution of stationary line and fibre processes.Adv. Appl. Prob. 33 (2001), 6–24 Zbl 0998.62080, MR 1825313, 10.1239/aap/999187894
Reference: [8] Mair B. A., Rao, M., Anderson J. M. M.: Positron emission tomography, Borel measures and weak convergence.Inverse Problems 12 (1996), 965–976 Zbl 0862.60098, MR 1421659
Reference: [9] Matheron G.: Random Sets and Integral Geometry.Wiley, New York 1975 Zbl 0321.60009, MR 0385969
Reference: [10] McLachlan G. J., Krishnan T.: The EM Algorithm and Extensions.Wiley, New York 1997 Zbl 1165.62019, MR 1417721
Reference: [11] Mecke J., Nagel W.: Stationäre räumliche Faserprozesse und ihre Schnittzahlrosen.Elektron. Informationsverarb. Kybernet. 16 (1980), 475–483 Zbl 0458.60047, MR 0619343
Reference: [12] Metropolis N., Rosenbluth A., Rosenbluth M., Teller, A., Teller E.: Equation of state calculations by fast computing machines.J. Chem. Phys. 21 (1953), 1087–1091 10.1063/1.1699114
Reference: [13] Meyn S., Tweedie R.: Markov Chains and Stochastic Stability.Springer, London 1993 Zbl 1165.60001, MR 1287609
Reference: [14] Schneider R.: Convex Bodies: The Brunn-Minkowski Theory.Encyclopedia Math. Appl. 44 (1993) Zbl 0798.52001, MR 1216521
Reference: [15] Stoyan D., Kendall W. S., Mecke J.: Stochastic Geometry and its Applications.Second edition. Wiley, New York 1995 Zbl 1155.60001, MR 0895588
Reference: [16] Tierney L.: Markov chains for exploring posterior distributions.Ann. Statist. 22 (1994), 1701–1762 Zbl 0829.62080, MR 1329166, 10.1214/aos/1176325750
Reference: [17] Wald A.: Statistical Decision Functions.Wiley, New York 1950 Zbl 0229.62001, MR 0036976


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