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Bayesian inference and model selection for stochastic epidemics

Periodic Reporting for period 1 - BERNADETTE (Bayesian inference and model selection for stochastic epidemics)

Reporting period: 2021-05-10 to 2023-05-09

The Marie Sklodowska-Curie Action (MSCA) titled “Bayesian inference and model selection for stochastic epidemics” (BERNADETTE) addressed the issue of developing novel statistical methodology for the modeling of transmission dynamics of infectious diseases like COVID-19. This work is driven by the challenges of under-ascertainment of COVID-19 infections and the presence of heterogeneity in type, relevance, and granularity of the data. No single dataset can provide enough information on its own to estimate disease transmission, but estimation is feasible by synthesizing multiple datasets. Bayesian evidence synthesis combines expert knowledge and multiple data sources like streams of surveillance data and ad-hoc studies in a coherent manner, linking different data sources through equations that describe how data sources, quantities under estimation, and model parameters relate to each other. The project focused on proposing Bayesian evidence synthesis approaches for the analysis of COVID-19 data, with the aim to: (i) infer the true number of infections using daily COVID-19 attributable mortality counts; (ii) learn the age-specific transmission rates; (iii) reconstruct the epidemic drivers from publicly available data sources.

The objectives of the BERNADETTE MSCA have been (i) the study of Bayesian evidence synthesis methods, identification of COVID-19 data sources, specification of an epidemic model for expressing transmission dynamics and selection of appropriate prior distributions for the time-varying model parameters; (ii) combination of the aforementioned components through a hierarchical model to develop a holistic framework for quantifying the effect of intervention measures and estimating key epidemiological parameters and implementation of the developed methodology to COVID-19 data from European countries; (iii) development of a statistical tool for improving computational efficiency and prediction accuracy; (iv) reproducibility of research. In parallel, the action aimed at ensuring further development of additional competencies that will be fundamental for the Fellow reaching a position of professional maturity.

The originality and innovative nature of BERNADETTE will contribute to healthcare research. Despite the substantial advancements in Bayesian evidence synthesis in the last few years, there is a need for model building strategies of increasing realism and complexity to better inform infection control policies. BERNADETTE proposes novel approaches for providing evidence-based knowledge of COVID-19 transmission while facilitating model realism and explainability, and for supporting healthcare services. The BERNADETTE outputs will assist in improving European preparedness planning and support decision-making in the framework of national epidemic preparedness plans.
Work performed during this Fellowship was ascribed to four specific work packages. The intention of WP1 was to study and identify Bayesian evidence synthesis methods and COVID-19 data sources to specify an epidemic model for expressing transmission dynamics and to propose appropriate prior distributions for expressing the dynamic nature of selected model parameters. A technical report that describes in detail the proposed Bayesian evidence synthesis framework was prepared, forming the central pillar of BERNADETTE. WP2 aimed to combine the components of WP1 though a hierarchical model to develop a holistic framework for quantifying the effect of intervention measures and forecasting future case number scenarios. The developed methodology would be implemented to COVID-19 data from European countries. We proposed modeling the age-dependent dynamics of COVID-19 via independent diffusion processes and demonstrated that this facilitates model realism and explainability compared to the state of the art. WP3 substantially expanded the research conducted in WP1-2 by augmenting the transmission model with time-dependent epidemiological parameters which were implemented as exchangeable diffusion processes. This will enable the researcher to incorporate a-priori beliefs that there is a shared structure between the age-dependent transmission dynamics of a disease. WP4 provided computational tools for making BERNADETTE accessible to end-users. The Bernadette R library for Bayesian analysis of infectious disease transmission dynamics is available at the Comprehensive R Archive Network ( The BERNADETTE Github repository ( contains a freely available interactive web-tool in the form of a Shiny application which can be activated from the package, aiming to visualize the model outputs.

The Fellow received research training in the fields of Epidemic modeling, Bayesian evidence synthesis methods, Analysis of disease outbreak data, Advanced Bayesian model selection and estimation, Probabilistic programming, and Development of web applications and R code libraries. He has been advising a full-time PhD student at AUEB since the start of his MSCA Fellowship. The student’s viva is scheduled, and on track, for August 2023. The Fellow further developed his management skills and provided leadership in publishing and leadership in research events like the organization of the workshop on Statistical modeling of epidemic outbreaks which aimed at Public Health policy makers, Epidemiologists, Statisticians and Data Scientists, as well as students working in these areas.

The results of BERNADETTE were reported in 3 papers (2 preprints under review, 1 manuscript in preparation). This work has been presented in 11 international conferences, meetings, seminars, and research workshops. The BERNADETTE research has been popularized via school visits and a presentation at the European Researcher’s Night 2022 in Athens, Greece. All activities were communicated via the project website ( Twitter (@BernadetteMsca) and LinkedIn (
The results contributed to the area of infectious disease epidemiology and are particularly timely considering the European Commission strategy for EU4Health 2021-2027, aiming to contribute to social progress and advance well-being of Europe’s citizens. We have developed novel statistical methodology for estimation of disease transmission and for the description of several aspects of the underlying infection pathway of a disease. The Bernadette software is gaining in popularity since its appearance on CRAN, with more than 1000 downloads ( since May 2023. The Bernadette R library has been included in the CRAN Task View on Epidemiology ( adding to the array of tools developed for infectious disease epidemiology using the R programming language. Two preprints are currently under review in high-impact peer review journals and one manuscript is under development. Additionally, the methodology developed in Work Package 3 will grow the number of functionalities of the Bernadette R library, making advanced analysis of disease dynamics more approachable for scientists interested in Public Health related questions and for Public Health policy makers. These activities will continue to achieve impact in coming years.
Statistical modeling of epidemic outbreaks workshop