Abstract: Daily precipitation has an enormous impact on human activity, and the study of how it varies over time and space, and what global indicators influence it, is of paramount importance to Australian agriculture. The topic is complex and would benefit from a common and publicly available statistical framework that scales to large data sets. We propose a general Bayesian spatio-temporal mixture model accommodating mixed discrete-continuous data. Our analysis uses over 294 million daily rainfall measurements since 1876, spanning 17,606 rainfall measurement sites. The size of the data calls for a parsimonious yet flexible model as well as computationally efficient methods for performing the statistical inference. Parsimony is achieved by encoding spatial, temporal and climatic variation entirely within a mixture model whose mixing weights depend on covariates. Computational efficiency is achieved by constructing a Markov chain Monte Carlo sampler that runs in parallel in a distributed computing framework. We present examples of posterior inference on short-term daily component classification, monthly intensity levels, offsite prediction of the effects of climate drivers and long-term rainfall trends across the entire continent. Computer code implementing the methods proposed in this paper is available as an R package.