One difficulty for real‐time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistical problems, infrastructure difficulties, and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast due to the use of the integrated nested Laplace approximation. The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and severe acute respiratory infection data in the state of Paraná, Brazil.

Tuberculosis poses a global health risk and Brazil is among the top twenty countries by absolute mortality. However, this epidemiological burden is masked by underreporting, which impairs planning for effective intervention. We present a comprehensive investigation and application of a Bayesian hierarchical approach to modelling and correcting under-reporting in tuberculosis counts, a general problem arising in observational count data. The framework is applicable to fully under-reported data, relying only on an informative prior distribution for the mean reporting rate to supplement the partial information in the data. true count generating process and the under-reporting mechanism, while also allowing for complex spatio-temporal structures. We present several sensitivity analyses based on simulation experiments to aid the elicitation of the prior distribution for the mean reporting rate and decisions relating to the inclusion of covariates. Both prior and posterior predictive model checking are presented, as well as a critical evaluation of the approach.

Household air pollution generated from the use of polluting cooking fuels and technologies is a major source of disease and environmental degradation in low- and middle-income countries. Using a novel modelling approach, we provide detailed global, regional and country estimates of the percentages and populations mainly using 6 fuel categories (electricity, gaseous fuels, kerosene, biomass, charcoal, coal) and overall polluting/clean fuel use – from 1990-2020 and with urban/rural disaggregation. Here we show that 53% of the global population mainly used polluting cooking fuels in 1990, dropping to 36% in 2020. In urban areas, gaseous fuels currently dominate, with a growing reliance on electricity; in rural populations, high levels of biomass use persist alongside increasing use of gaseous fuels. Future projections of observed trends suggest 31% will still mainly use polluting fuels in 2030, including over 1 billion people in Sub-Saharan African by 2025.

In many fields and applications count data can be subject to delayed reporting. This is where the total count, such as the number of disease cases contracted in a given week, may not be immediately available, instead arriving in parts over time. For short term decision making, the statistical challenge lies in predicting the total count based on any observed partial counts, along with a robust quantification of uncertainty.In this article we discuss previous approaches to modelling delayed reporting and present a multivariate hierarchical framework where the count generating process and delay mechanism are modelled simultaneously. Unlike other approaches, the framework can also be easily adapted to allow for the presence of under-reporting in the final observed count. To compare our approach with existing frameworks, one of which we extend to potentially improve predictive performance, we present a case study of reported dengue fever cases in Rio de Janeiro. Based on both within-sample and out-of-sample posterior predictive model checking and arguments of interpretability, adaptability, and computational efficiency, we discuss the advantages and disadvantages of each modelling framework.