Open-source indicators have been proposed as a way of tracking and forecasting disease outbreaks. Some, such are meteorological data, are readily available as reanalysis products. Others, such as those derived from our online behavior (web searches, media article etc.) are gathered easily and are more timely than public health reporting. In this study we investigate how these datastreams may be combined to provide useful epidemiological information. The investigation is performed by building data assimilation systems to track influenza in California and dengue in India. The first does not suffer from incomplete data and was chosen to explore disease modeling needs. The second explores the case when observational data is sparse and disease modeling complexities are beside the point. The two test cases are for opposite ends of the disease tracking spectrum. We find that data assimilation systems that produce disease activity maps can be constructed. Further, being able to combine multiple open-source datastreams is a necessity as any one individually is not very informative. The data assimilation systems have very little in common except that they contain disease models, calibration algorithms and some ability to impute missing data. Thus while the data assimilation systems share the goal for accurate forecasting, they are practically designed to compensate for the shortcomings of the datastreams. Thus we expect them to be disease and location-specific.
A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least-square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the flutter speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. In conclusion, it will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision.
Monte Carlo (MC) sampling is a common method used to randomly sample a range of scenarios. The associated error follows a predictable rate of convergence of $1/\sqrt{N}$, such that quadrupling the sample size halves the error. This method is often employed in performing global sensitivity analysis which computes sensitivity indices, measuring fractional contributions of uncertain model inputs to the total output variance. In this study, several models are used to observe the rate of decay in the MC error in the estimation of the conditional variance, the total variance in the output, and the global sensitivity indices. The purpose is to examine the rate of convergence of the error in existing specialized, albeit MC-based, sampling methods for estimation of the sensitivity indices. It was found that the conditional variances and sensitivity indices all follow the $1/\sqrt{N}$ convergence rate. Future work will test the convergence of observables from more complex models such as ignition time in combustion.