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Dimension Reduction in Extended Quermass-Interaction Process

Author

Listed:
  • Kateřina Staňková Helisová

    (Czech Technical University in Prague)

  • Jakub Staněk

    (Charles University in Prague)

Abstract

Many objects studied in biology, medicine or material sciences create spatial formations of random shape in which we can observe mutual interactions among those objects. In order to analyse the data composed of such patterns, we use the methods of spatial statistics. Recently, extended random-disc Quermass-interaction process was studied, simulated and consequently statistically analysed using MCMC maximum likelihood method (MCMC MLE). However, this analysis brought some problems. First, it was quite time-consuming, secondly, in some special cases, the parameter estimates may undervalue the real parameter values. In this paper, we describe how we can solve these problems by dimension reduction.

Suggested Citation

  • Kateřina Staňková Helisová & Jakub Staněk, 2014. "Dimension Reduction in Extended Quermass-Interaction Process," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 355-368, June.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9343-x
    DOI: 10.1007/s11009-013-9343-x
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    References listed on IDEAS

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    1. Jesper Møller & Kateřina Helisová, 2010. "Likelihood Inference for Unions of Interacting Discs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 365-381, September.
    2. Mrkvicka, T. & Rataj, J., 2008. "On the estimation of intrinsic volume densities of stationary random closed sets," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 213-231, February.
    3. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2012. "Spatio-Temporal Model for a Random Set Given by a Union of Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 883-894, September.
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