6. Modelling Conditional Densities Using Finite Smooth Mixtures

  1. Kerrie L. Mengersen4,
  2. Christian P. Robert5 and
  3. D. Michael Titterington6
  1. Feng Li1,
  2. Mattias Villani2 and
  3. Robert Kohn3

Published Online: 24 APR 2011

DOI: 10.1002/9781119995678.ch6

Mixtures: Estimation and Applications

Mixtures: Estimation and Applications

How to Cite

Li, F., Villani, M. and Kohn, R. (2011) Modelling Conditional Densities Using Finite Smooth Mixtures, in Mixtures: Estimation and Applications (eds K. L. Mengersen, C. P. Robert and D. M. Titterington), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119995678.ch6

Editor Information

  1. 4

    School of Mathematical Sciences, Queensland University of Technology, Australia

  2. 5

    Université Paris-Dauphine, CEREMADE, Paris, France

  3. 6

    University of Glasgow, Glasgow, UK

Author Information

  1. 1

    Department of Statistics, Stockholm University, Sweden

  2. 2

    Sveriges Riksbank, Stockholm, Sweden

  3. 3

    Australian School of Business, University of New South Wales, Sydney, Australia

Publication History

  1. Published Online: 24 APR 2011
  2. Published Print: 15 APR 2011

ISBN Information

Print ISBN: 9781119993896

Online ISBN: 9781119995678



  • modelling conditional densities - using finite smooth mixtures;
  • finite smooth mixtures, or mixtures of experts (ME) - knowing machine learning literature;
  • smooth mixtures, capable of approximating - large class of conditional distributions;
  • simple-and-many versus complex-and-few - modelling regression data-skewed response variable;
  • inference methodology - general MCMC scheme;
  • generalised linear model (GLM) - to variable selection case;
  • model comparison - components assumed known in MCMC scheme;
  • simulation study in Villani et al. (2009) - smooth mixture of homoscedastic Gaussian components for heteroscedastic data;
  • LIDAR data, first real dataset - using laser-emitted light to detect chemical compounds in atmosphere;
  • log predictive density score (LPDS) - fivefold cross-validation of electricity expenditure data


This chapter contains sections titled:

  • Introduction

  • The model and prior

  • Inference methodology

  • Applications

  • Conclusions

  • Acknowledgements

  • Appendix: Implementation details for the gamma and log-normal models

  • References