Understanding how decision makers balance operational efficiency with environmental and ecological risks is central to vessel navigation. We model vessel speed as a control variable in a constrained optimization framework in which vessel operators balance multiple competing objectives, including transit efficiency, ice related navigational risk, and whale related ecological risk. The underlying risk parameters are estimated using over 14 million Automatic Identification System (AIS) observations from the United States Arctic (2010-2019), together with environmental covariates and spatially explicit whale density estimates. The framework incorporates a nonlinear risk objective, vessel heterogeneity, and regularization to ensure stable and interpretable results.The inferred trade offs reveal distinct decision making patterns across vessel groups and navigational statuses. Vessel types such as Tug Tow and Cargo balance operational speed with environmental and ecological considerations. In contrast, several vessel groups, including Fishing, Passenger, and Unspecified vessels, are strongly influenced by ice related risk, while Pleasure Craft and Tankers exhibit higher sensitivity to whale related risk. Across navigational status categories, similar heterogeneity is observed. The dominant status, under way using engine, displays a clear trade off, whereas other statuses, such as aground and undefined, are strongly shaped by ice related constraints. Statuses including restricted maneuverability and engaged in fishing exhibit higher estimated sensitivity to whale related risk, though with substantial uncertainty.Sensitivity analysis indicates that increasing whale-related risk weighting produces limited changes in model-implied optimal speed, whereas increasing ice-related risk leads to more consistent reductions.

Social media platforms hold valuable insights, yet extracting essential information can be challenging. Traditional top-down approaches often struggle to capture critical signals in rapidly changing events. As global events evolve swiftly, social media narratives, including instances of disinformation, become significant sources of insights. To address the need for an inductive strategy, we explore a niche social media platform GAB and an established messaging service Telegram, to develop methodologies applicable on a broader scale. This study investigates narrative evolution on these platforms using quantitative corpus-based discourse analysis techniques. Our approach is a novel mode to study multiple social media domains to distil key information which may be obscured otherwise, allowing for useful and actionable insights. The paper details the technical and methodological aspects of gathering and preprocessing GAB and Telegram data for a keyness (Log Ratio) metric analysis, identifying crucial nouns and verbs for deeper exploration. Empirically, this approach is applied to a case study of a well defined event that had global impact: the 2023 Wagner mutiny. The main findings are: (1) the time line can be deconstructed to provide useful data features allowing for improved interpretation; (2) a methodology is applied which provides a basis for generalization. The key contribution is an approach, that in some cases, provides the ability to capture the dynamic narrative shifts over time with elevated confidence. The approach can augment near-real-time assessment of key social movements, allowing for informed governance choices. This research is important because it lays out a useful methodology for time series relevant info-culling, which can enable proactive modes for positive social engagement.

Model misspecification is a long-standing enigma of the Bayesian inference framework as posteriors tend to get overly concentrated on ill-informed parameter values towards the large sample limit. Tempering of the likelihood has been established as a safer way to do updates from prior to posterior in the presence of model misspecification. At one extreme tempering can ignore the data altogether and at the other extreme it provides the standard Bayes' update when no misspecification is assumed to be present. However, it is an open issue how to best recognize misspecification and choose a suitable level of tempering without access to the true generating model. Here we show how probabilistic classifiers can be employed to resolve this issue. By training a probabilistic classifier to discriminate between simulated and observed data provides an estimate of the ratio between the model likelihood and the likelihood of the data under the unobserved true generative process, within the discriminatory abilities of the classifier. The expectation of the logarithm of a ratio with respect to the data generating process gives an estimation of the negative Kullback-Leibler divergence between the statistical generative model and the true generative distribution. Using a set of canonical examples we show that this divergence provides a useful misspecification diagnostic, a model comparison tool, and a method to inform a generalised Bayesian update in the presence of misspecification for likelihood-based models.