A logging-while-drilling density sensor includes a gamma ray source and at least two NaI detectors spaced apart from the source for determining measurements indicative of the formation density. An analytic function based on a heuristic model is used to predict the measured response as a function of offset, mud density and formation density. The model may be used to provide a caliper measurement where acoustic caliper data are unreliable. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understand that it will not be used to interpret or limit the scope or meaning of the claims. 37 CFR 1.72(b).