The application of maximum entropy to the calculation of drug absorption rates was introduced in an earlier paper. Here it is developed further, and the whole procedure is presented as a problem in scientific inference to be solved using Bayes' theorem. Blood samples do not need to be taken at equally spaced intervals, and no smoothing, interpolation, extrapolation, or other preprocessing of the data is necessary. The resulting input rate estimates are smooth and physiologically realistic, even with noisy data, and their accuracy is quantified. Derived quantities such as the proportion of the dose absorbed, and the mean and median absorption times, are also obtained, together with their error estimates. There are no arbitrarily valued parameters in the analysis, and no specific functional form, such as an exponential or polynomial, is assumed for the input rate functions.