The combination of large open data sources with machine learning approaches presents a potentially powerful way to predict events such as protest or social unrest. However, accounting for uncertainty in such models, particularly when using diverse, unstructured datasets such as social media, is essential to guarantee the appropriate use of such methods. Here we develop a Bayesian method for predicting social unrest events in Australia using social media data. This method uses machine learning methods to classify individual postings to social media as being relevant, and an empirical Bayesian approach to calculate posterior event probabilities. We use the method to predict events in Australian cities over a period in 2017/18.