SignificanceForecasts routinely provide critical information for dangerous weather events but not yet for epidemics. Researchers develop computational models that can be used for infectious disease forecasting, but forecasts have not been broadly compared or tested. We collaboratively compared forecasts from 16 teams for 8 y of dengue epidemics in Peru and Puerto Rico. The comparison highlighted components that forecasts did well (e.g., situational awareness late in the season) and those that need more work (e.g., early season forecasts). It also identified key facets to improve forecasts, including using multiple model ensemble approaches to improve overall forecast skill. Future infectious disease forecasting work can build on these findings and this framework to improve the skill and utility of forecasts.

A unified approach to attractor reconstruction Louis M. Pecora Code 6362, Naval Research Laboratory, Washington, D.C. 20375 Linda MonizDepartment of Mathematics, Trinity College, Washington, D.C. 20017 Jonathan Nichols Code 5673, Naval Research Laboratory, Washington, D.C. 20375 Thomas L. Carroll In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e., attractor reconstruction. The process has focused primarily on intuitive, heuristic, and empirical arguments for selection of the key embedding parameters, delay and embedding dimension. This approach has left several longstanding, but common problems unresolved in which the standard approaches produce inferior results or give no guidance at all. We view the current reconstruction process as unnecessarily broken into separate problems. We propose an alternative approach that views the problem of choosing all embedding parameters as being one and the same problem addressable using a single statistical test formulated directly from the reconstruction theorems. This allows for varying time delays appropriate to the data and simultaneously helps decide on embedding dimension. A second new statistic, undersampling, acts as a check against overly long time delays and overly large embedding dimension. Our approach is more flexible than those currently used, but is more directly connected with the mathematical requirements of embedding. In addition, the statistics developed guide the user by allowing optimization and warning when embedding parameters are chosen beyond what the data can support. We demonstrate our approach on uni-and multivariate data, data possessing multiple time scales, and chaotic data. This unified approach resolves all the main issues in attractor reconstruction. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2430294͔What is the requirement for the determination of vector components for the reconstruction of an attractor from time series? This is a problem that has been studied for many years and everyone agrees that the problem consists of finding time delay, embedding dimension, and in the multivariate case which time series to use for each coordinate (although the latter is a much neglected problem). Most work has arbitrarily divided the problem into finding the delay and embedding dimension, separately. This division is the source of many problems. In addition, almost all approaches, and there are many, rely on weak heuristic methods or a choice of arbitrary scales (e.g., what constitutes a false neighbor) which are usually unknown. We view the construction of vectors for attractor reconstruction as a problem in finding a coordinate system to represent the dynamical state. What is mathematically necessary for any good coordinate system is that the coordinates be independent; this requirement is highlighted in Taken's theorem. To this end we develop a statistic to test for general, nonlinear functional dependence called the continuity s...

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BackgroundIn the 2015 NOAA Dengue Challenge, participants made three dengue target predictions for two locations (Iquitos, Peru, and San Juan, Puerto Rico) during four dengue seasons: 1) peak height (i.e., maximum weekly number of cases during a transmission season; 2) peak week (i.e., week in which the maximum weekly number of cases occurred); and 3) total number of cases reported during a transmission season. A dengue transmission season is the 12-month period commencing with the location-specific, historical week with the lowest number of cases. At the beginning of the Dengue Challenge, participants were provided with the same input data for developing the models, with the prediction testing data provided at a later date.MethodsOur approach used ensemble models created by combining three disparate types of component models: 1) two-dimensional Method of Analogues models incorporating both dengue and climate data; 2) additive seasonal Holt-Winters models with and without wavelet smoothing; and 3) simple historical models. Of the individual component models created, those with the best performance on the prior four years of data were incorporated into the ensemble models. There were separate ensembles for predicting each of the three targets at each of the two locations.Principal findingsOur ensemble models scored higher for peak height and total dengue case counts reported in a transmission season for Iquitos than all other models submitted to the Dengue Challenge. However, the ensemble models did not do nearly as well when predicting the peak week.ConclusionsThe Dengue Challenge organizers scored the dengue predictions of the Challenge participant groups. Our ensemble approach was the best in predicting the total number of dengue cases reported for transmission season and peak height for Iquitos, Peru.