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Recent outbreaks of Mpox and Ebola, and worrying waves of COVID-19, influenza and respiratory syncytial virus, have all led to a sharp increase in the use of epidemiological models to estimate key epidemiological parameters. The feasibility of this estimation task is known as the practical identifiability (PI) problem. Here, we investigate the PI of eight commonly reported statistics of the classic susceptible–infectious–recovered model using a new measure that shows how much a researcher can expect to learn in a model-based Bayesian analysis of prevalence data. Our findings show that the basic reproductive number and final outbreak size are often poorly identified, with learning exceeding that of individual model parameters only in the early stages of an outbreak. The peak intensity, peak timing and initial growth rate are better identified, being in expectation over 20 times more probable having seen the data by the time the underlying outbreak peaks. We then test PI for a variety of true parameter combinations and find that PI is especially problematic in slow-growing or less-severe outbreaks. These results add to the growing body of literature questioning the reliability of inferences from epidemiological models when limited data are available. 

Abstract Citizen-generated counter speech is a promising way to fight hate speech and promote peaceful, non-polarized discourse. However, there is a lack of large-scale longitudinal studies of its effectiveness for reducing hate speech. To this end, we perform an exploratory analysis of the effectiveness of counter speech using several different macro- and micro-level measures to analyze 180,000 political conversations that took place on German Twitter over four years. We report on the dynamic interactions of hate and counter speech over time and provide insights into whether, as in ‘classic’ bullying situations, organized efforts are more effective than independent individuals in steering online discourse. Taken together, our results build a multifaceted picture of the dynamics of hate and counter speech online. While we make no causal claims due to the complexity of discourse dynamics, our findings suggest that organized hate speech is associated with changes in public discourse and that counter speech—especially when organized—may help curb hateful rhetoric in online discourse. 

Abstract Empirical measurements of ecological networks such as food webs and mutualistic networks are often rich in structure but also noisy and error-prone, particularly for rare species for which observations are sparse. Focusing on the case of plant–pollinator networks, we here describe a Bayesian statistical technique that allows us to make accurate estimates of network structure and ecological metrics from such noisy observational data. Our method yields not only estimates of these quantities, but also estimates of their statistical errors, paving the way for principled statistical analyses of ecological variables and outcomes. We demonstrate the use of the method with an application to previously published data on plant–pollinator networks in the Seychelles archipelago and Kosciusko National Park, calculating estimates of network structure, network nestedness, and other characteristics. 

The Border Gateway Protocol (BGP) is a distributed protocol that manages interdomain routing without requiring a centralized record of which autonomous systems (ASes) connect to which others. Many methods have been devised to infer the AS topology from publicly available BGP data, but none provide a general way to handle the fact that the data are notoriously incomplete and subject to error. This paper describes a method for reliably inferring AS-level connectivity in the presence of measurement error using Bayesian statistical inference acting on BGP routing tables from multiple vantage points. We employ a novel approach for counting AS adjacency observations in the AS-PATH attribute data from public route collectors, along with a Bayesian algorithm to generate a statistical estimate of the AS-level network. Our approach also gives us a way to evaluate the accuracy of existing reconstruction methods and to identify advantageous locations for new route collectors or vantage points. 

Abstract Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error prone and unreliable. A fundamental problem in empirical network science is how to make the best possible estimates of network structure given such unreliable data. In this article, we describe a fully Bayesian method for reconstructing networks from observational data in any format, even when the data contain substantial measurement error and when the nature and magnitude of that error is unknown. The method is introduced through pedagogical case studies using real-world example networks, and specifically tailored to allow straightforward, computationally efficient implementation with a minimum of technical input. Computer code implementing the method is publicly available.