Why We Need a Bayesian Approach to Early Detection of Epidemic Outbreaks and Financial Bubbles Using First-Order Autoregressive Models with Structural Changes

We propose a Bayesian alternative to the frequentist approach developed in our NESUG 2007/2008 and SGF 2008 presentations. This approach includes first-order autoregression modeling, estimating autoregression parameters, building confidence intervals and hypothesis testing. For the purpose of early detection, this statistical inference is performed daily using short samples of previous observations. The results obtained within the frequentist approach are important, however, this approach suffers from well-known downward bias and related asymmetric distribution of classic least square estimates of autoregression parameters, so that standard methods for constructing confidence intervals based on symmetry are inaccurate. In our Bayesian alternative, we can avoid these disadvantages. Additionally, everyday testing results in a multiplicity problem and requires some adjustment, which is not always effective within the frequentist approach. In contrast, the current consensus suggests that correct adjusting is automatic within the Bayesian paradigm and that Bayesian testing of many hypotheses does not pose problems different than testing a single hypothesis, so no adjustment is needed. In addition, no resampling testing is necessary, which makes Bayesian detection procedures faster than frequentist counterparts. The Bayesian framework allows us to incorporate prior and any other type of exogenous information, which can compensate for the shortness of everyday baseline samples. Bayesian methods provide naturally interpretable results: they output the posterior probability that an outbreak has occurred. We can sound the alarm whenever posterior probability of an outbreak exceeds some threshold. The intended audience: SAS users of all levels who work with SAS®/STAT and SAS®/ETS.