Abstract
The matrixt distribution is derived and its properties are shown which are applied for the Bayesian inference in the multivariate linear model. By this approach hypothesis tests for the multivariate model are derived which are less sensitive than the tests of the sampling theory. Examples of their application in the analysis of data for the detection of deformations are given.
Similar content being viewed by others
References
J.D. BOSSLER: Bayesian Inference in Geodesy. Dissertation. The Ohio State University, Columbus, Ohio, 1972.
G.E.P. BOX and G.C. TIAO: Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, Mass., 1973.
E.A. CORNISH: The multivariate t-distribution associated with a set of normal sample deviates. Australian Journal of Physics, 7, pp. 531–542, 1954.
J.M. DICKEY: Matricvariate generalizations of the multivariate t distribution and the inverted multivariate t distribution. The Annals of Mathematical Statistics, 38, pp. 511–518, 1967.
C.W. DUNNETT and M. SOBEL: A bivariate generalization of Student's t-distribution, with tables for certain special cases. Biometrika, 41, pp. 153–169, 1954.
S. GEISSER: Bayesian estimation in multivariate analysis. The Annals of Mathematical Statistics, 36, pp. 150–159, 1965.
J. HARTIGAN: Invariant prior distributions. The Annals of Mathematical Statistics, 35, pp. 836–845, 1964.
H. JEFFREYS: Theory of Probability. Carendon Press, Oxford, 1961.
A.M. KSHIRSAGAR: Some extensions of the multivariate t-distribution and the multivariate generalization of the distribution of the regression coefficient. Proceedings of the Cambridge Philosophical Society, 57, pp. 80–85, 1960.
K.R. KOCH: Parameterschätzung und Hypothesentests in linearen Modellen. Dümmler, Bonn, 1980.
K.R. KOCH: Statistical tests for detecting crustal movements using Bayesian inference. NOAA Technical Report NOS NGS 29, National Geodetic Survey, National Ocean Service, Rockville, Md., 1984.
K.R. KOCH: Ein statistisches Auswerteverfahren für deformationsmessungen. Allgemeine Vermessungs-Nachrichten, 92, pp. 97–108, 1985.
K. RIESMEIER: Test von Ungleichungshypothesen in linearen Modellen mit Bayes-Verfahren. Deutsche Geodätische Kommission, C, 292, München, 1984.
A. ZELLNER: An Introduction to Bayesian Inference in Econometrics. Wiley, New York, 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koch, K.R., Riesmeier, K. Bayesian inference for the derivation of less sensitive hypothesis tests. Bull. Geodesique 59, 167–179 (1985). https://doi.org/10.1007/BF02520608
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02520608