Gomez-Villegas, Miguel Angel and Main Yaque, Paloma and Sanz San Miguel, Luis (2009) A Bayesian Analysis For The Multivariate Point Null Testing Problem. Statistics, 43 (4). pp. 379-391. ISSN 0233-1888
Restricted to Repository staff only until 2020.
A Bayesian test for the point null testing problem in the multivariate case is developed. A procedure to get the mixed distribution using the prior density is suggested. For comparisons between the Bayesian and classical approaches, lower bounds on posterior probabilities of the null hypothesis, over some reasonable classes of prior distributions, are computed and compared with the p-value of the classical test. With our procedure, a better approximation is obtained because the p-value is in the range of the Bayesian measures of evidence.
|Uncontrolled Keywords:||posterior probability; multivariate point null hypothesis; p-value; mixed prior distributions|
|Subjects:||Sciences > Mathematics > Mathematical statistics|
C.R. Rao, Test of significance in multivariate analysis, Biometrika 35 (1948), pp. 58–79.
N.H. Timm, Multivariate Analysis with Applications in Education And Psychology, Brooks/Cole, Belmont,California, 1975.
J.O. Berger and M. Delampady, Testing precise hypotheses, Statist. Sci. 3 (1987), pp. 317–352.
J.O. Berger, B. Boukai, andY.Wang, Unified frequentist and bayesian testing of a precise hypothesis, Statist. Sci. 3(1997), pp. 133–160.
Downloaded by [Biblioteca Universidad Complutense de Madrid] at 04:20 03 May 2012 390 M.A. Gómez–Villegas et al. M.S. Oh, A Bayes test for simple versus one–sided hypotheses on the mean vector of a multivariate normal
distribution, Commun. Statist. Theory Meth. 27(10) (1998), pp. 2371–2389.
H.S. Oh and A. DasGupta, Comparison of the p-value and posterior probability, J. Statist. Plann. Inference 76(1999), pp. 93–107.
T. Sellke, M.J. Bayarri, and J. Berger, Calibration of p-values for testing precise null hypotheses, Amer. Statist. 55 (2001), pp. 62–71.
A. O’Hagan, Properties of intrinsic and fractional Bayes factors, Test 6(1) (1997), pp. 101–118.
J.B. Berger and L.R. Pericchi, Training samples in objective Bayesian model selection, Ann. Statist. 32(3)(2004),pp. 841–869.
M.A. Gómez–Villegas and E. Gómez Sánchez–Manzano, Bayes factor in testing precise hypotheses, Commun. Statist. Theory Meth. 21(6) (1992), pp. 1707–1715.
M.A. Gómez–Villegas and L. Sanz, Reconciling Bayesian and frequentist evidence in the point null testing problem, Test 7(1) (1998), pp. 207–216.
M.A. Gómez–Villegas and L. Sanz, ε–contaminated priors in testing point null hypotheses: a procedure to determine the prior probability, Statist. Probab. Lett. 47(1) (2000), pp. 53–60.
M.A. Gómez–Villegas, P. Maín, and L. Sanz, A suitable Bayesian approach in testing point null hypothesis: some examples revisited, Commun. Statist. Theory Meth. 31(2)(2002), pp. 201–217.
M.A. Gómez–Villegas, P. Maín, L. Sanz, and H. Navarro, Asymptotic relationships between posterior probabilities and p-values using the hazard rate, Statist. Probab. Lett. 66(1) (2004), pp. 59–66.
M.A. Gómez–Villegas, and B. González–Pérez, Bayesian analysis of contingency tables, Commun. Statist. Theory Meth. 34 (2005), pp. 1743–1754.
J.M. Bernardo and A.F.M. Smith, Bayesian Theory, JohnWiley and Son, NewYork, 1994.
T.W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability
inequalities, Proc. Amer. Math. Soc. 6 (1955), pp. 170–176.
D.R. Jensen and I.J. Good, A representation for ellipsoidal distributions, Siam J. Appl. Math. 43(5) (1983), pp. 1194–1200.
G. Casella and R.L. Berger, Reconciling Bayesian and frequentist evidence in the one-sided testing problem (with discussion), J. Amer. Statist. Assoc. 82 (1987), pp. 106-135.
G.P. Frets, Heredity of head form in man, Genetica 3(1921), pp. 193–200.
Y.L. Tong, The Multivariate Normal Distribution, Springer Verlag, NewYork, 1990.
|Deposited On:||19 Jun 2012 09:36|
|Last Modified:||06 Feb 2014 10:29|
Repository Staff Only: item control page