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Robust HPD Regions in Bayesian Regression Models


  • Potzelberger, Klaus
  • Polasek, Wolfgang


A Bayesian analysis of the linear regression model with only parts of the prior distribution specified or a robust Bayesian analysis lead to sets of posterior distributions. E. E. Leamer (1978) describes the region of posterior means for conjugate priors and varying prior covariance matrices. As an extension to Bayesian confidence sets (HPD regions) the authors introduce the concept of HiFi (high fiduciary) regions. The Hifi region is a union of HPD regions and is a tool for describing the dependence of the posterior distribution on the prior covariance. The authors assume that the prior covariance matrix varies in an interval of matrices. Copyright 1991 by The Econometric Society.

Suggested Citation

  • Potzelberger, Klaus & Polasek, Wolfgang, 1991. "Robust HPD Regions in Bayesian Regression Models," Econometrica, Econometric Society, vol. 59(6), pages 1581-1589, November.
  • Handle: RePEc:ecm:emetrp:v:59:y:1991:i:6:p:1581-89

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    References listed on IDEAS

    1. Lucas, Robert E, Jr & Prescott, Edward C, 1971. "Investment Under Uncertainty," Econometrica, Econometric Society, vol. 39(5), pages 659-681, September.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    4. Epstein, Larry G, 1983. " Aggregating Quasi-Fixed Factors," Scandinavian Journal of Economics, Wiley Blackwell, vol. 85(2), pages 191-205.
    5. Takeo Hoshi & Anil Kashyap & David Scharfstein, 1990. "Bank Monitoring and Investment: Evidence from the Changing Structure of Japanese Corporate Banking Relationships," NBER Chapters,in: Asymmetric Information, Corporate Finance, and Investment, pages 105-126 National Bureau of Economic Research, Inc.
    6. Takeo Hoshi & Anil K. Kashyap & David Scharfstein, 1989. "Bank monitoring and investment: evidence from the changing structure of Japanese corporate banking relations," Finance and Economics Discussion Series 86, Board of Governors of the Federal Reserve System (U.S.).
    7. Schiantarelli, F. & Georgoutsos, D., 1990. "Monopolistic competition and the Q theory of investment," European Economic Review, Elsevier, vol. 34(5), pages 1061-1078, July.
    8. Fumio Hayashi, 1991. "Taxes and Corporate Investment in Japanese Manufacturing," NBER Chapters,in: Productivity Growth in Japan and the United States, pages 295-316 National Bureau of Economic Research, Inc.
    9. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-224, January.
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    Cited by:

    1. John Aldrich, 2006. "When are inferences too fragile to be believed?," Journal of Economic Methodology, Taylor & Francis Journals, vol. 13(2), pages 161-177.
    2. Meczarski, Marek & Zielinski, Ryszard, 1997. "Stability of the posterior mean in linear models An admissibility property of D-optimum and E-optimum designs," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 117-123, April.

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