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BAYESIAN INFERENCES ON NONLINEAR FUNCTIONS OF

THE PARAMETERS IN LINEAR REGRESSION

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A. J. VAN DER MERWE, C. A. VAN DER MERWE AND P. C. N. GROENEWALD

*Department of Mathematical Statistics, University of the Orange Free State,*

P.O. Box 339, Bloemfontein 9300, South Africa
(Received December 25, 1989; revised September 25, 1990)

**Abstract.**
A variety of statistical problems (e.g. the
*x*-intercept in
linear regression, the abscissa of the point of intersection of two simple
linear
regression lines or the point of extremum in quadratic regression) can be
viewed as
questions of inference on nonlinear functions of the parameters in the general
linear regression model. In this paper inferences on the threshold
temperatures and
summation constants in crop development will be made. A Bayesian approach
for the
general formulation of this problem will be developed. By using numerical
integration, credibility intervals for individual functions as well as for
linear
combinations of the functions of the parameters can be obtained. The
implementation
of an odds ratio procedure is facilitated by placing a proper prior on the
ratio of
the relevant parameters.

*Key words and phrases*:
Bayesian inferences, threshold
temperatures,
summation constants, regression, intervals of highest posterior density,
posterior
odds ratio.

**Source**
( TeX ,
DVI ,
PS )