Modelling Conditional Probability Distributions for Periodic Variables

  • Christopher M. Bishop
  • Ian T. Nabney
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 8)


Most conventional techniques for estimating conditional probability densities are inappropriate for applications involving periodic variables. In this paper we introduce three related techniques for tackling such problems, and test them using synthetic data. We then apply them to the problem of extracting the distribution of wind vector directions from radar scatterometer data.


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  1. [1]
    C M Bishop, Mixture density networks. Technical Report NCRG/4288, Neural Computing Research Group, Aston University, U.K. (1994).Google Scholar
  2. [2]
    C. M. Bishop, Neural Networks for Pattern Recognition. Oxford University Press (1995).Google Scholar
  3. [3]
    C. M. Bishop and C. Legleye, Estimating conditional probability distributions for periodic variables, in: D. S. Touretzky, G. Tesauro, and T. K. Leen, editors, Advances in Neural Information Processing Systems, Vol. 7 (1995), pp641–648, Cambridge MA, MIT Press.Google Scholar
  4. [4]
    R A Jacobs, M I Jordan, S J Nowlan, and G E Hinton, Adaptive mixtures of local experts, Neural Computation, Vol. 3 (1991), pp79–87.CrossRefGoogle Scholar
  5. [5]
    Y Liu, Robust neural network parameter estimation and model selection for regression, in: Advances in Neural Information Processing Systems, Vol.6 (1994), pp192–199, Morgan Kaufmann.Google Scholar
  6. [6]
    K V Mardia, Statistics of Directional Data. Academic Press, London (1972).MATHGoogle Scholar
  7. [7]
    G J McLachlan and K E Basford, Mixture models: Inference and Applications to Clustering. Marcel Dekker, New York (1988).MATHGoogle Scholar
  8. [8]
    S Thiria, C Mejia, F Badran, and M Crepon, A neural network approach for modeling nonlinear transfer functions: Application for wind retrieval from spaceborne scatterometer data, Journal of Geophysical Research, Vol. 98(C12) (1993), pp22827–22841.CrossRefGoogle Scholar
  9. [9]
    D M Titterington, A F M Smith, and U E Makov, Statistical Analysis of Finite Mixture Distributions, John Wiley, Chichester (1985).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Christopher M. Bishop
    • 1
  • Ian T. Nabney
    • 1
  1. 1.Neural Computing Research GroupAston UniversityBirminghamUK

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