Some remarks on the use of improper priors for the analysis of exponential regression models

We consider Bayesian inference on the exponential regression model. It is known that standard improper priors on the parameters of this model lead to marginal posterior distributions on one of the parameters involved which are also improper on the interval (0, 1). This has sometimes been interpreted as meaning that the observations are irrelevant. We re-analyse this problem using a finitely-additive approach and show that the above conclusion is not generally correct. This result emphasizes, once again, the dangers of routine approach to Bayesian inference using improper priors.