Incorporating shape information is essential for the delineation of many organs and anatomical structures in medical images. While previous work has mainly focused on parametric spatial transformations applied to reference template shapes, in this paper, we address the Bayesian inference of parametric shape models for segmenting medical images with the objective of providing interpretable results. The proposed framework defines a likelihood appearance probability and a prior label probability based on a generic shape function through a logistic function. A reference length parameter defined in the sigmoid controls the trade-off between shape and appearance information. The inference of shape parameters is performed within an Expectation-Maximisation approach in which a Gauss-Newton optimization stage provides an approximation of the posterior probability of the shape parameters. This framework is applied to the segmentation of cochlear structures from clinical CT images constrained by a 10-parameter shape model. It is evaluated on three different datasets, one of which includes more than 200 patient images. The results show performances comparable to supervised methods and better than previously proposed unsupervised ones. It also enables an analysis of parameter distributions and the quantification of segmentation uncertainty, including the effect of the shape model.