Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Choosing the Tuning Constant by Laplace Approximation

  • Ahn, Sung-Mahn (College of Business Administration, Kookmin University) ;
  • Kwon, Suhn-Beom (College of Business Administration, Kookmin University)
  • Received : 2012.03.04
  • Accepted : 2012.04.27
  • Published : 2012.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

Evidence framework enables us to determine the tuning constant in a penalized likelihood formula. We apply the framework to the estimating parameters of normal mixtures. Evidence, which is a solely data-dependent measure, can be evaluated by Laplace approximation. According to a synthetic data simulation, we found that the proper values of the tuning constant can be systematically obtained.

Keywords

References

  1. Ahn, S. and Baik, S. W. (2011). Estimating parameters in multivariate normal mixtures, Korean Communications in Statistics, 18, 357-366. https://doi.org/10.5351/CKSS.2011.18.3.357
  2. Chickering, D. M. and Heckerman, D. (1997). Efficient approximations for the marginal likelihood of Bayesian networks with hidden variables, Machine Learning, 29, 181-212. https://doi.org/10.1023/A:1007469629108
  3. Eggermont, P. P. B. and LaRiccia, V. N. (2001). Maximum Penalized Likelihood Estimation, Springer.
  4. Good, I. J. (1971). A nonparametric roughness penalty for probability densities, Nature, 229, 29-30.
  5. Good, I. J. and Gaskins, R. A. (1971). Nonparametric roughness penalties for probability densities, Biometrika, 58, 255-277. https://doi.org/10.1093/biomet/58.2.255
  6. MacKay, D. J. C. (1992). Bayesian interpolation, Neural Computation, 4, 415-447. https://doi.org/10.1162/neco.1992.4.3.415
  7. Marron, J. S. and Wand, M. P. (1992). Exact mean integrated squared error, Annals of Statistics, 20, 712-736. https://doi.org/10.1214/aos/1176348653
  8. Raftery, A. (1995). Bayesian model selection in social research. In Marsden, P. (Ed.), Sociological Methodology, Blackwells, Cambridge, MA.
  9. Xu, L. and Jordan, M. I. (1996). On convergence properties of the EM algorithm for Gaussian mixtures, Neural Computation, 8, 129-151. https://doi.org/10.1162/neco.1996.8.1.129