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.

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We present a noise-injected version of the expectation–maximization (EM) algorithm: the noisy expectation–maximization (NEM) algorithm. The NEM algorithm uses noise to speed up the convergence of the EM algorithm. The NEM theorem shows that additive noise speeds up the average convergence of the EM algorithm to a local maximum of the likelihood surface if a positivity condition holds. Corollary results give special cases when noise improves the EM algorithm. We demonstrate these noise benefits on EM algorithms for three data models: the Gaussian mixture model (GMM), the Cauchy mixture model (CMM), and the censored log-convex gamma model. The NEM positivity condition simplifies to a quadratic inequality in the GMM and CMM cases. A final theorem shows that the noise benefit for independent identically distributed additive noise decreases with sample size in mixture models. This theorem implies that the noise benefit is most pronounced if the data is sparse.

Feedback fuzzy cognitive maps (FCMs) can model the complex structure of public support for insurgency and terrorism (PSOT). FCMs are fuzzy causal signed digraphs that model degrees of causality in interwoven webs of feedback causality and policy variables. Their nonlinear dynamics permit forward-chaining inference from input causes and policy options to output effects. We show how a concept node causally affects downstream nodes through a weighted product of the intervening causal edge strengths. FCMs allow users to add detailed dynamics and feedback links directly to the causal model. Users can also fuse or combine FCMs from multiple experts by weighting and adding the underlying FCM fuzzy edge matrices. The combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample. Statistical or machine-learning algorithms can use numerical sample data to learn and tune a FCM’s causal edges. A differential Hebbian learning law can approximate a PSOT FCM’s directed edges of partial causality using time-series training data. The PSOT FCM adapts to the computational factor-tree PSOT model that Davis and OMahony based on prior social science research and case studies. Simulation experiments compare the PSOT models with the adapted FCM models.