On Flexible Bayesian Test Criteria for Nested Point Null Hypotheses of Multiple Regression Coefficients

  • Jae-Hyun Kim (Assistant Professor, Department of Applied Statistics, Seokyeong University, Seoul 136-704, Korea) ;
  • Hea-Jung Kim (Professor, Department of Statistics, Dongguk University, Seoul 100-715, Korea)
  • Published : 1996.12.01

Abstract

As flexible Bayesian test criteria for nested point null hypotheses of multiple regression coefficients, partial and overall Bayes factors are introduced under a class of intuitively meaningful prior. The criteria lead to a simple method for considering different prior beliefs on the subspaces that constitute a partition of the coefficient parameter space. A couple of tests are suggested based on the criteria. It is shown that they enable us to obtain pairwise comparisons of hypotheses of the partitioned subspaces. Through a Monte Carlo simulation, performance of the tests based on the criteria are compared with the usual Bayesian test (based on Bayes factor)in terms of their respective powers.

Keywords

References

  1. Regression Analysis: Theory, Methods, and Applications Sen, A.;Srivastava, M.
  2. Statistical Decision Theory and Bayesion Analysis Berger, J. O.
  3. Statistical Science v.2 Comment On Testing Precise Hypotheses Zellner, A.;J. O. Berger;M. Delampady
  4. Journal of the American Statistical Association v.90 Multiple Bayes Factors for Testing Hypotheses Bertolino, F.;Piccinato, L.;Racugno, W.
  5. Journal of Statistical Planning and Inferece v.25 Robust Bayesian Analysis: Sensitivity to the Prior Berger, J. O.
  6. Bayesian Statistics : An introduction Lee, P. E.
  7. Journal of The American Statistical Association v.82 Testing A Point Null Hypotheses : The Irreconcilability of P Values and Evidence, (With Discussion) Berger, J. O.;Sellke, T.
  8. Theory of Probability(3rd. ed.) Jeffreys, H.