The general probability distribution for the fractional amount of a geophysical parameter contained within a finite transect has been published previously. On the basis of this information confidence intervals were placed on the observed fraction prior to measurement from knowledge of the underlying distributions for the length of geophysical regions and of the gaps between such regions. In this form, hypothesis testing of models for these length distributions could be made given the observed fraction. However, what is also required (for change detection, for example) is the confidence interval for the true fraction given the observed fraction. Such a reversal of distribution may be provided by Bayes' theorem, as is demonstrated here for the case of underlying exponential distributions for these lengths. As an example, this is applied to transects across cloud fields observed by GMS-5, revealing that confidence intervals for the true cloud fraction, given the observed fraction, can be rather broad over typical climate model grid scales. This is an important result given the current number of proposed satellite-borne missions that are to make transect measurements of cloud parameters, in part to enhance such models. ¿ 2001 American Geophysical Union