This paper addresses the problem of 3D human body shape and pose estimation from RGB images. Some recent approaches to this task predict probability distributions over human body model parameters conditioned on the input images. This is motivated by the ill-posed nature of the problem wherein multiple 3D reconstructions may match the image evidence, particularly when some parts of the body are locally occluded. However, body shape parameters in widely-used body models (e.g. SMPL) control global deformations over the whole body surface. Distributions over these global shape parameters are unable to meaningfully capture uncertainty in shape estimates associated with locallyoccluded body parts. In contrast, we present a method that (i) predicts distributions over local body shape in the form of semantic body measurements and (ii) uses a linear mapping to transform a local distribution over body measurements to a global distribution over SMPL shape parameters. We show that our method outperforms the current stateof-the-art in terms of identity-dependent body shape estimation accuracy on the SSP-3D dataset, and a private dataset of tape-measured humans, by probabilistically-combining local body measurement distributions predicted from multiple images of a subject.