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Analyzing user messages in social media can measure different population characteristics, including public health measures. For example, recent work has correlated Twitter messages with influenza rates in the United States; but this has largely been the extent of mining Twitter for public health. In this work, we consider a broader range of public health applications for Twitter. We apply the recently introduced Ailment Topic Aspect Model to over one and a half million health related tweets and discover mentions of over a dozen ailments, including allergies, obesity and insomnia. We introduce extensions to incorporate prior knowledge into this model and apply it to several tasks: tracking illnesses over times (syndromic surveillance), measuring behavioral risk factors, localizing illnesses by geographic region, and analyzing symptoms and medication usage. We show quantitative correlations with public health data and qualitative evaluations of model output. Our results suggest that Twitter has broad applicability for public health research.