Bayesian strategies for Causal Graphs: Translating Theory into Practice

Elucidating causal mechanisms is a central objective across many sciences. Probabilistic and causal graphical models provide a fitting framework for representing and analysing complex relationships among variables. Given a causal diagram integrated with structural models, we may answer interventional or counterfactual questions. Establishing which variables exert a causal influence on which other is a more demanding task. Causal discovery aims to find plausible causal relationships with little to no prior knowledge about the graphical structure, a broad and fast-moving field. 
 
The Bayesian paradigm offers a principled and natural framework for quantifying the model uncertainty and incorporating prior domain knowledge. Along with the availability of rich data sources, computational advances in the last decades now enable larger-scale Bayesian approaches to causal discovery. Answering real-world questions requires bridging the gap between sophisticated theoretical developments and their practical implementation. The task poses unique and often under-appreciated challenges in dealing with all facets of the data, finding a good balance between idealised and realistic scenarios, and integrating expertise from multiple disciplines.
 
Drawing upon real-world case studies in the life sciences, we will explore the current landscape of Bayesian methods for causal structure learning and effect estimation from observational data, examining the underlying assumptions and limitations of the operational approaches available. Finally, we will reflect on the most promising future directions, covering the most pressing problems we need to solve to accelerate the translational value of Bayesian inference for causal graphs in advancing science.



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