In the era of big data, huge volumes of data are generated from online social networks, sensor networks, mobile devices, and organizations’ enterprise systems. This phenomenon provides organizations with unprecedented opportunities to tap into big data to mine valuable business intelligence. However, traditional business analytics methods may not be able to cope with the flood of big data. The main contribution of this paper is the illustration of the development of a novel big data stream analytics framework named BDSASA that leverages a probabilistic language model to analyze the consumer sentiments embedded in hundreds of millions of online consumer reviews. In particular, an inference model is embedded into the classical language modeling framework to enhance the prediction of consumer sentiments. The practical implication of our research work is that organizations can apply our big data stream analytics framework to analyze consumers’ product preferences, and hence develop more effective marketing and production strategies.