Advertisement

A bayesian approach to binary response curve estimation

  • Makio Ishiguro
  • Yosiyuki Sakamoto
Article

Summary

The purpose of the present paper is to propose a practical procedure for the estimation of the binary response curve. The procedure is based on a model which approximates the response curve by a finely segmented piecewise constant function. To obtain a stable estimate we assume a prior distribution of the parameters of the model. The prior distribution has several parameters (hyper-parameters) which are chosen to minimize an information criterion ABIC. The procedure is applicable to data consisting of observations of a binary response variable and a single explanatory variable. The practical utility of the procedure is demonstrated by examples of applications to the dose response curve estimation, to the intensity function estimation of a point process and to the analysis of social survey data. The application of the procedure to the discriminant analysis is also briefly discussed.

Keywords

Discriminant Analysis Prior Distribution BAYESIAN Approach Final Estimate True Function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Akaike, H. (1980). Likelihood and Bayes procedure,Bayesian Statistics (eds. J. M. Bernardo, M. H. De Groot, D. U. Lindley and A. F. M. Smith), University Press, Valencia, Spain.MATHGoogle Scholar
  2. [2]
    Akaike, H. and Ishiguro, M.. (1980). Trend estimation with missing observations,Ann. Inst. Statist. Math.,32, B, 481–488.CrossRefGoogle Scholar
  3. [3]
    Cox, D. R. (1970)Analysis of Binary Data: Methuen & Co. Ltd., LondonMATHGoogle Scholar
  4. [4]
    Ishiguro, M. and Akaike, H. (1981). A Bayesian approach to the trading-day adjustment of monthly data.Time Series Analysis (eds. O. D. Anderson and M. R. Perryman), North-Holland, Amsterdam.Google Scholar
  5. [5]
    Ishiguro, M. and Sakamoto, Y.. (1982). A Bayesian approach to probability density estimation,Research Memorandum No. 239, The Institute of Statistical Mathematics, Tokyo.MATHGoogle Scholar
  6. [6]
    Kashiwagi, N. (1982). A Bayesian estimation procedure for fertilities in field experiments,Research Memorandum No. 220, The Institute of Statistical Mathematics, Tokyo.Google Scholar
  7. [7]
    Lewis, P. A. W. (1964). A branching Poisson process model for the analysis of computer failure patterns.J. R. Statist. Soc., B,26, 398–456.MathSciNetMATHGoogle Scholar
  8. [8]
    Mays, C. W. and Lloyed, R. D. (1971). Bone sarcoma risk from90Sr, Biomedical Implications of Radiostrontium Exposure (eds. M. Goldman and L. K. Bustad),AEC Sympo.,25, 354.Google Scholar
  9. [9]
    Mays, C. W. and Lloyed R. D.. (1972). Bone sarcoma incidence vs. alpha particle dose,Radiobiology of Plutonium (eds. B. J. Stover and W. S. S. Jee), J. W. Press, Salt Lake City.Google Scholar
  10. [10]
    Nakamura, T. (1982). A Bayesian cohort model for standard cohort table analysis,Proc. Inst. Statist. Math.,29, 77–79 (in Japanese).MATHGoogle Scholar
  11. [11]
    Noda, K. and Murakami, M. (1979). Estimation of two-phase segmented lines on the basis of binary data.J. Japan Statist. Soc.,12, 63–75.MathSciNetMATHGoogle Scholar
  12. [12]
    Ozaki, T.. (1981). Marked point processes and non-linear systems modeling of daily rainfall and riverflow time series in stochastic hydrology,Technical Report, No. 148, Department of Mathematics, University of Manchester, Institute of Science and Technology, Manchester.Google Scholar
  13. [13]
    Sakamoto, Y. and Akaike, H.. (1978). Anaysis of cross-classified data by AIC,Ann. Inst. Statist. Math. 30, B, 185–197.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Sakamoto, Y. (1983). Efficient use of Akaike's Information Criterion for model selection in high dimensional contingency table analysis,Metron (to appear).Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1983

Authors and Affiliations

  • Makio Ishiguro
  • Yosiyuki Sakamoto

There are no affiliations available

Personalised recommendations