<p><strong>Abstract.</strong> Observational constraints on the equilibrium climate sensitivity have been generated in a variety of ways, but the epistemic basis of these calculations have not always been clearly presented and a number of results have been calculated which appear to be based on somewhat informal heuristics. This causes a lack of clarity about the status of such results and how they compare to other analyses, in particular whether the differences between them may be due to differences in unstated assumptions rather than observational evidence.</p> <p>In this paper, we show how these problems can be resolved. We demonstrate that many of these estimates can be reinterpreted within the standard subjective Bayesian framework in which a prior over the uncertain parameters is updated through a likelihood arising from observational evidence. In many of these cases, the prior which was (under this interpretation) implicitly used exhibits some unconventional and possibly undesirable properties. We present alternative calculations which use the same observational information to update a range of explicitly presented priors.</p> <p>Our calculations suggest that the heuristic methods do often generate reasonable results, in that they agree fairly well with the explicitly Bayesian approach using a reasonable prior. However, we also find some significant differences and argue that the explicitly Bayesian approach is preferred, as it both clarifies the role of the prior, and allows researchers to transparently test the sensitivity of their results to it.</p>