2020/09/11 by J. Baxter, Baxter, Jonathan
Mathematics · #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2009.05446
openalex publication_date 2020/09/11 · openalex created_date 2020/09/21 · openalex updated_date 2026/07/28
Following [Diggle 2011, Greenland 1995], we give a simple formula for the Bayesian posterior density of a prevalence parameter based on unreliable testing of a population. This problem is of particular importance when the false positive test rate is close to the prevalence in the population being tested. An efficient Monte Carlo algorithm for approximating the posterior density is presented, and applied to estimating the Covid-19 infection rate in Santa Clara county, CA using the data reported in [Bendavid 2020]. We show that the true Bayesian posterior places considerably more mass near zero, resulting in a prevalence estimate of 5,000--70,000 infections (median: 42,000) (2.17% (95CI 0.27%--3.63%)), compared to the estimate of 48,000--81,000 infections derived in [Bendavid 2020] using the delta method. A demonstration, with code and additional examples, is available at testprev.com.