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The format of this document is essentially "two papers in one," with the first chapter focusing on mostly theoretical considerations (although illustrated with an example), while the second chapter provides a practical, real-world example presented in the form of a tutorial.
Methods of Causal Inference: We will first introduce the reader to the idea of formal causal inference using the well-known example of Simpson\’s Paradox. Secondly, we will provide a brief summary of the Neyman-Rubin model, which represents a traditional statistical approach in this context. Once this method is established as a reference point, we will introduce two methods within the Bayesian network paradigm, Pearl\’s Do-Operator, which is based on "Graph Surgery", and a method based on "Likelihood Matching" algorithm (LM). LM allows fixing probability distributions and can be considered as a probabilistic extension of statistical matching.
Practical Applications of Direct Effects and Causal Inference: While our treatment of Neyman-Rubin is limited to the first chapter, the two Bayesian network-based methods will be further illustrated as practical applications in the second chapter. Special weight will be given to Likelihood Matching (LM), as it has not yet been documented in literature. We will explain the practical benefits of LM with a real-world business application and discuss observational and causal inference in the context of a marketing mix model. Using the marketing mix model as the principal example, we will go into greater detail regarding the analysis workflow, so the reader can use this example as a step-by-step guide to implementing such a model with BayesiaLab.