Interpretable Bayesian Learning
for Physical and Engineering Sciences

ABS Schools

The Applied Bayesian Statistics summer school has been running since 2004. It is organised by IMATI CNR Istituto di Matematica Applicata e Tecnologie Informatiche, Consiglio Nazionale delle Ricerche, Milano.

The school is organized in cooperation with Fondazione "Alessandro Volta"

The school aims to present state-of-the-art Bayesian applications, inviting leading experts in their field.
Each year a different topic is chosen.

Past editions were devoted to: Spatio-temporal Methods in Environmental Epidemiology, Bayesian Phylogenetics and Infectious Diseases, Bayesian Causal Inference, Gene Expression Genomics, Decision Modelling in Health Care, Spatial Data in Environmental and Health Sciences, Bayesian Methods and Econometrics, Bayesian Decision Problems in Biostatistics and Clinical Trials, Bayesian Methodology for Clustering, Classification and Categorical Data Analysis, Bayesian Machine Learning with Biomedical Applications, Hierarchical Modeling for Environmental Processes, Stochastic Modelling for Systems Biology, Bayesian Methods for Variable Selection with Applications to High-Dimensional Data and Applied Bayesian Nonparametrics, Modern Bayesian Methods and Computing for the Social Sciences, Bayes Big Data and the Internet, Modeling Spatial And Spatio-Temporal Data With Environmental Applications, Bayesian Statistical Modelling and Analysis in Sport, Bayesian Demography.

The lecturer is Prof. Simon Mak (Department of Statistical Science, Duke University), a leading expert in integrating domain knowledge (e.g., scientific theories, mechanistic models, guiding principles) as prior information for cost-efficient statistical inference, prediction, and decision-making. He serves as Program Chair-Elect of the ASA Section on Physical and Engineering Sciences and has received major honors including the j-ISBA Blackwell-Rosenbluth Award and the ASA SPES Award.

The practical lectures will be given by Yen-Chun Liu (Department of Statistical Science, Duke University), a brilliant PhD student of Prof. Mak, specializing in Bayesian optimization, Gaussian processes, and reinforcement learning.

The topic chosen for the 2026 school is
Interpretable Bayesian Learning for Physical and Engineering Sciences.

This course investigates the rising topic of interpretable statistical learning, motivated by timely needs from modern scientific and engineering applications. For such applications, state-of-the-art machine learning methods often yield analyses that are uninterpretable to scientists, which greatly obfuscates scientific findings and decision-making. Interpretable Bayesian learning provides an elegant and effective solution by embedding scientific principles (e.g., boundary conditions, mechanistic equations) within its prior specification.
In this course, we will cover a broad spectrum of interpretable Bayesian learning methods (with theory and algorithms), providing a cohesive roadmap for this recent and rapidly-evolving area of study. This will be complemented by practical case studies from ongoing projects in particle physics, mechanical engineering, and bioengineering. Emphasis will be made on novel directions for research in this promising area.

Topics will cover

• Fundamentals of Gaussian process (GP) surrogate modeling: prediction, parameter inference, experimental design
• Decision-making with GP surrogates: Bayesian optimization, active learning, Bayesian inverse problems
• Markov Chain Monte Carlo (MCMC) methods
• Boundary-informed GP modeling
• Shape-constrained (e.g., monotone, isotonic, convex) GP modeling
• Mechanistic GP modeling
• Physics-integrated neural networks, its Bayesian variants and recent developments
• Dynamical system recovery: SINDy, Bayesian SINDy, and recent developments