Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-20T01:27:17.518Z Has data issue: false hasContentIssue false
  • English
  • Français

Hierarchical probability models and Bayesian analysis of mine locations

Part of: Decision theory Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Noel Cressie  and
Andrew B. Lawson
Noel Cressie*
Affiliation:
Ohio State University
Andrew B. Lawson*
Affiliation:
University of Aberdeen
*
∗ Postal address: Department of Statistics, The Ohio State University, 1958 Neil Avenue, Columbus OH43210, USA.
∗∗ Postal address: Department of Mathematical Sciences, University of Aberdeen, King's College, Old Aberdeen, UK. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Based on remote sensing of a potential minefield, point locations are identified, some of which may not be mines. The mines and mine-like objects are to be distinguished based on their point patterns, although it must be emphasized that all one sees is the superposition of their locations. In this paper, we construct a hierarchical spatial point-process model that accounts for the different patterns of mines and mine-like objects and uses posterior analysis to distinguish between them. Our Bayesian approach is applied to minefield data obtained from a multispectral video remote-sensing system.

Keywords

Cox point processMarkov chain Monte CarloPoisson point processposterior distributionprior distribution

MSC classification

Primary: 60G55: Point processes
Secondary: 62C05: General considerations
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 315 - 330
Copyright
Copyright © Applied Probability Trust 2000 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Besag, J., Green, P., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems. Statist. Sci. 10, 3–66.Google Scholar
Byers, S. and Raftery, A. (1998). Nearest neighbor clutter removal for estimating features in spatial point processes. J. Amer. Statist. Assoc. 93, 577–584.CrossRefGoogle Scholar
Cowles, M. K. and Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: a comparative review. J. Amer. Statist. Assoc. 91, 883–904.Google Scholar
Cressie, N. (1993). Statistics for Spatial Data, revised edn. John Wiley, New York.CrossRefGoogle Scholar
Cressie, N. and Lawson, A. B. (1998). Bayesian hierarchical analysis of minefield data. In Detection and Remediation Technologies of Mines and Minelike Targets III: SPIE Proc. Vol. 3392. SPIE, Bellingham, WA, pp. 930–940.CrossRefGoogle Scholar
Diggle, P. and Rowlingson, B. (1994). A conditional approach to point process modelling of elevated risk. J. Roy. Statist. Soc. A 157, 433–440.CrossRefGoogle Scholar
Geyer, C. and {Møller}, J. (1994). Simulation procedures and likelihood inference for spatial point processes. Scand. J. Statist. 21, 84–88.Google Scholar
Green, P. J. (1995). Reversible jump MCMC computation and Bayesian model determination. Biometrika 82, 711–732.CrossRefGoogle Scholar
Holmes, Q. A., Schwartz, C. R., Seldin, J., Wright, J. and Wieter, L. J. (1995). Adaptive multispectral CFAR detection of land mines. In Detection and Remediation Technologies for Mines and Minelike Targets: SPIE Proc. Vol. 2496. SPIE, Bellingham, WA, pp. 421–432.Google Scholar
Lake, D., Sadler, B. and Casey, S. (1997). Detecting regularity in minefields using collinearity and a modified Euclidian algorithm. In Detection and Remediation Technologies for Mines and Minelike Targets II: SPIE Proc. Vol. 3079. SPIE, Bellingham, WA, pp. 500–507.CrossRefGoogle Scholar
Lawson, A. B. (1996). Markov chain Monte Carlo methods for spatial cluster processes. In Computer Science and Statistics: Proceedings of the Interface Vol. 27, pp. 314–319.Google Scholar
Lawson, A. B. (1997). Some spatial statistical tools for pattern recognition. In Quantitative Approaches in Systems Analysis, Vol. 7, eds Stein, A., de Vries, F. W. T. P. and Schut, J. C. T. de Wit Graduate School for Production Ecology, pp. 43–58.Google Scholar
Lawson, A. B. and Clark, A. (1999). Markov chain Monte Carlo methods for putative sources of hazard and general clustering. In Disease Mapping and Risk Assessment for Public Health, eds Lawson, A. B., Böhning, D, Lesaffre, E., Biggeri, A., Viel, J.-F. and Bertollini, R. John Wiley, New York, Chapter 9, pp. 119–141.Google Scholar
van Lieshout, M. and Baddeley, A. (1995). Markov chain Monte Carlo methods for clustering of image features. In Proc. 5th IEEE Int. Conf. Image Processing Appl. IEEE Conf. Publ. 410. IEEE, New York, pp. 241–245.Google Scholar
Muise, R. and Smith, C. (1995). A linear density algorithm for patterned minefield detection. In Detection and Remediation Technologies for Mines and Minelike Targets: SPIE Proc. Vol. 2496. SPIE, Bellingham, WA, pp. 583–593.Google Scholar
Priebe, C. E., Olson, T. E. and Healy, D. M. (1997). Exploiting stochastic partitions for minefield detection. In Detection and Remediation Technologies for Mines and Minelike Targets II: SPIE Proc. Vol. 3079. SPIE, Bellingham, WA, pp. 508–518.Google Scholar
Ripley, B. D. (1988). Statistical Inference for Spatial Processes. Cambridge University Press, Cambridge, UK.Google Scholar
Witherspoon, N., Holloway, J., Davis, K., Millar, R. and Dubey, A. (1995). The coastal battlefield reconnaisance and analysis COBRA program for minefield detection. In Detection and Remediation Technologies for Mines and Minelike Targets: SPIE Proc. Vol. 2496. SPIE, Bellingham, WA, pp. 500–508.Google Scholar