The human gut microbiome has been shown to be associated with a variety of human diseases, including cancer, metabolic conditions and inflammatory bowel disease. Current approaches for detecting microbiome associations are limited by relying on specific measures of ecological distance, or only allowing for the detection of associations with individual bacterial species, rather than the whole microbiome. In this work, we develop a novel hierarchical Bayesian model for detecting global microbiome associations. Our method is not dependent on a choice of distance measure, and is able to incorporate phylogenetic information about microbial species. We perform extensive simulation studies and show that our method allows for consistent estimation of global microbiome effects. Additionally, we investigate the performance of the model on two real-world microbiome studies: a study of microbiome-metabolome associations in inflammatory bowel disease, and a study of associations between diet and the gut microbiome in mice. We show that we can use the method to reliably detect associations in real-world datasets with varying numbers of samples and covariates.