The Infant Mortality Rate (IMR) is an important population health statistic often used as one of the indicators of the health status of a nation. In many countries lacking adequate vital registration systems, sample methods are used to estimate IMRs. However, evaluations of this approach are rare and the literature contains no assessments of the stochastic uncertainty underlying these estimated IMRs. Stochastic uncertainty reflects the fact that even where the underlying IMR is constant in a small population over time, there is a likelihood of yearly fluctuation in its empirical observations even if it is measured from a complete count of the events of interest. In this study a method is presented that can be used to assess this stochastic uncertainty. We use the country of Ghana as a case study for this purpose. The method, a beta-binomial model, is described, tested for validity, and illustrated using 2014 sample-based estimates of IMR for 13 sample regions in Ghana. As such, the approach we described regarding the revision of sample-based IMR estimates is aimed at taking into account of the stochastic uncertainty while preserving the information concerning the uncertainty due to sampling. In applying the method to Ghana, we find that the sample-based IMR estimates perform well in accounting for stochastic uncertainty and could be applied elsewhere.