Knowledge bases (KBs) about notable entities and their properties are an important asset in applications such as search, question answering and dialogue. All popular KBs capture virtually only positive statements, and abstain from taking any stance on statements not stored in the KB. This paper makes the case for explicitly stating salient statements that do not hold. Negative statements are useful to overcome limitations of question answering systems that are mainly geared for positive questions; they can also contribute to informative summaries of entities. Due to the abundance of such invalid statements, any effort to compile them needs to address ranking by saliency. We present a statisticalinference method for compiling and ranking negative statements, based on expectations from positive statements of related entities in peer groups. Experimental results, with a variety of datasets, show that the method can effectively discover notable negative statements, and extrinsic studies underline their usefulness for entity summarization. Datasets and code are released as resources for further research.