Bayesian Mixture Models: A Blood‐Free Dissection of a Sheep

Abstract

The use of computed tomography (CT) scanning to measure attributes of tissue composition in animal experiments has grown steadily since the early 1990s. This technology is used on a range of experiments, such as nutrition trials for live animals, as well as on carcases after slaughter. A CT scan returns measurements averaged over a pixel area that represent the denseness of the tissue. This tissue denseness is related to tissue type, with fat being generally less dense then muscle and bone being the most dense tissue we study. However, tissue denseness is not well separated, leading to a large overlap on the boundaries between types. Normal mixture models have proved to be an efficient analytical technique for estimating the proportion of tissue types in individual CT scans, with MCMC output providing measures of variability that are unavailable in the standard cut-point modelling approach. These models are then used in conjunction with integration techniques to estimate the tissue volumes within a carcase. In this paper we initially model individual scan data using a hierarchical mixture model, where skewed tissue densities are represented by the addition of two or more components.The mixture model is then extended to account for some of the spatial information using a Markov random field represented by a Potts model in terms of the allocation vector. A scheme for choosing starting values for component parameters is presented. The paper concludes with the use of the Cavalieri approach to combine individual scan estimates in order to estimate the carcase volume.