### Impacto

Gomez-Villegas, Miguel Angel and Gonzalez-Perez, B.
(2011)
*A Bayesian Analysis For The Homogeneity Testing Problem Using Epsilon-Contaminated Priors.*
Communications in statistics. Theory and methods, 40
(6).
pp. 1049-1062.
ISSN 0361-0926

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Official URL: http://www.tandfonline.com/doi/pdf/10.1080/03610920903520547

## Abstract

In this article the problem of testing if r populations have the same distribution from a Bayesian perspective is studied using r × s contingency tables and ϵ–contaminated priors. A procedure to build a mixed prior distribution is introduced and a justification for this construction based on a measure of discrepancy is given. A lower bound for the posterior probabilities of the homogeneity null hypothesis, when the prior is in the class of ϵ–contaminated distributions, is calculated and compared numerically with the usual p-value. Examples show that the discrepancy between both is more acute when the mass assigned to the null in the mixed prior distribution is 0.5

Item Type: | Article |
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Uncontrolled Keywords: | Epsilon-Contaminated Priors; Contingency Tables; Homogeneity Testing Problem; P-Values; Posterior Probabilities;Point Null Hypothesis; P-Values; Frequentist Evidence; Contingency-Tables; Posterior Measures; Distributions;Statistics & Probability |

Subjects: | Sciences > Mathematics > Mathematical statistics |

ID Code: | 16042 |

References: | Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer. Berger, J. O. (1994). An overview over robust Bayesian analysis (with discussion). Test 3:5–124. Berger, J. O., Berliner, L. M. (1986). Robust Bayes and empirical Bayes analysis with e–contaminated priors. Ann. Statist. 14(2):461–486. Berger, J. O., Boukai, B., Wang, Y. (1999). Simultaneous bayesian-frequentist sequential testing of nested hypothesis. Biometrika 86:79–92. Berger, J. O., Dedlampady, M. (1987). Testing precise hyphotheses, (with discussion). Statist. Science 2(3):317–352. Berger, J. O., Sellke, T. (1987). Testing a point null hyphotesis: The irreconciliability of p-values and evidence, (with discussion). J. Amer. Statist. Assoc. 82:112–139. Casella, G., Berger, R. L. (1987). Reconciling bayesian and frequentist evidence in the one-sided testing problem, (with discussion). J. Amer. Statist. Assoc. 82:106–135. Delampady, M., Berger, J. O. (1990). Lower bounds on Bayes factors for multinomial distributions, with application to chi-squared tests of fit. Ann. Statist. 18(3):1295–1316. De la Horra, J. (2005). Reconciling classical and prior predictive p-values in the two sided location parameter testing problem. Commun. Statist. Theor. Meth. 34:575–583. Gómez-Villegas, M. A., Gómez, E. (1992). Bayes factor in testing precise hyphoteses. Commun. Statist. Theor. Meth. 21:1707–1715. Gómez-Villegas, M. A., González-Pérez, B. (2005). Bayesian analysis of contingency tables. Commun. Statist. Theor. Meth. 34(8):1743–1754. Gómez-Villegas, M. A., González-Pérez, B. (2006). A condition to obtain the same decision in the homogeneity testing problem from the frequentist and Bayesian point of view. Commun. Statist. Theor. Meth. 35:2211–2222. Gómez-Villegas, M. A., González-Pérez, B. (2008). e–Contaminated priors in contingency tables. Test 17(1):163–178. Gómez-Villegas, M. A., Maín, P., Sanz, L. (2002). A suitable Bayesian approach in testing point nullmnhypothesis: some examples revisited. Commun. Statist. Theor. Meth. 31(2):201–217. Gómez-Villegas, M. A., Maín, P., Sanz, L. (2004). A Bayesian analysis for the multivariate point null testing problem. Tech. Rep. Dpto. EIO, Universidad Complutense de Madrid 04-01. Gómez-Villegas, M. A., Maín, P., Sanz, L., Navarro, H. (2004). Asymptotic relationships between posterior probabilities and p-values using the hazard rate. Statist. Probab. Lett. 66:59–66. Gómez-Villegas, M. A., Sanz, L. (1998). Reconciling Bayesian and frequentist evidence in the point null testing problem. Test 7(1):207–216. Gómez-Villegas, M. A., Sanz, L. (2000). e-contaminated priors in testing point null hypothesis:a procedure to determine the prior probability. Statist. Probab. Lett. 47:53–60. Ghosh, J. K., Mukerjee, R. (1992). Non-informative priors. In: Bernardo, J. M., Berger, J. O., Dawid, A. P., Smith, A. F. M. eds. Bayesian Statistics, 4. Oxford: University Press, pp. 195–210 (with discussion). Homogeneity Testing Problem 1061 Downloaded by [Biblioteca Universidad Complutense de Madrid] at 03:35 07 May 2012 Huber, P. J. (1973). The use of Choquet capacities in statistics. Bull. Int. Statist. Inst. 45: 181–191. Lindley, D. V. (1957). A statistical paradox. Biometrika 44:187–192. Lindley, D. V. (1988). Statistical inference concerning Hardy-Weinberg equilibrium. Bayesian Statist. 3:307–326. McCulloch, R. E., Rossi, P. E. (1992). Bayes factors for non-linear hypothesis and likelihood distributions. Biometrika 79:663–676. Mukhopadhyay, S., Dasgupta, A. (1997). A uniform approximation of bayes solutions and posteriors: Frequentistly valid bayes inference. Statist. Decis. 15:51–73. Sellke, T., Bayarri, M. J., Berger, O. (2001). Calibration of p values for testing precise null hypotheses. Amer. Statistician 55(1):62–71. Sivaganesan, S. (1988). Range of posterior measures for priors with arbitrary contaminations. Commun. Statist. Theor. Meth. 17:1591–1612. Sivaganesan, S., Berger, J. (1989). Ranges of posterior measures for priors with unimodal contaminations. Ann. Statist. 17(2):868–889. 1062 Gómez-Villeges and González-Pérez Downloaded |

Deposited On: | 24 Jul 2012 10:00 |

Last Modified: | 06 Feb 2014 10:37 |

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