Bayesian inference provides a rigorous framework for combining data with prior knowledge to estimate parameters in complex models. However, the role and construction of priors is often insufficiently addressed in practice. Reported parameter values in the literature rarely include estimation uncertainty, making it difficult to construct informative priors. Additionally informative priors bare the risk of introducing potential misleading bias. In such cases, objective or uninformative priors may be preferable. Therefore, the overarching goal is to understand and control the influence of prior assumptions to ensure that priors support rather than distort Bayesian inference. For this, case studies from chemical process simulation will be used.
About Division 2.2 at BAM
In division 2.2, research focuses on the development of dynamic process models to describe all system states from start-up to shutdown, supported by an open library of dynamic, pressure-driven models. The division uses machine learning, uncertainty quantification and hybrid modeling methods to drive forward real-time application and plant monitoring. For the comprehensive digitalization of process engineering, the division is also researching information and data modelling as well as process models from engineering to the operation of chemical plants. This is supplemented by the development of methods for the safe and optimal transformation of chemical plants.
This master's thesis will focus on three key research questions:
1. Quantifying prior influence:
How can we quantify the effect of prior on the posterior?
2. Constructing objective priors for Bayesian inference:
How can uninformative or objective priors be designed or approximated to be compatible with modern inference techniques?
3. Building informative priors from literature data:
How can reported parameter values be translated into meaningful prior distributions and when is this preferable to use objective priors?
Task Description:
• Review of literature on methods for assessing prior impact as well as objective and weakly informative priors
• Evaluation and comparison of methods for quantifying prior influence on the posterior
• Development of uninformative/objective priors suitable for modern Bayesian inference techniques
• Development of methods to construct informative priors from reported parameter values
• Apply the developed methods to chemical engineering case studies to benchmark prior choices
Preferred Knowledge and Skills:
• Strong interest in statistics, Bayesian inference, or parameter estimation
• Basic programming skills in Python or a comparable scientific language
• Willingness to learn modern probabilistic modeling tools
Supervision and Environment: The project is situated in the areas of Bayesian inference, uncertainty quantification and data-driven modeling. Depending on the student’s interests, the thesis can be tailored toward a more theoretical or application-oriented focus.
Start: immediately
Contact:
Stefan Tönnis, M.Sc.
stefan.toennis@bam.de