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Randomised field experiments, such as A/B testing, have long been the gold standard for evaluating software changes. In the automotive domain, running randomised field experiments is not always desired, possible, or even ethical. In the face of such limitations, we develop a framework BOAT (Bayesian causal modelling for ObvservAtional Testing), utilising observational studies in combination with Bayesian causal inference, in order to understand real-world impacts from complex automotive software updates and help software development organisations arrive at causal conclusions. In this study, we present three causal inference models in the Bayesian framework and their corresponding cases to address three commonly experienced challenges of software evaluation in the automotive domain. We develop the BOAT framework with our industry collaborator, and demonstrate the potential of causal inference by conducting empirical studies on a large fleet of vehicles. Moreover, we relate the causal assumption theories to their implications in practise, aiming to provide a comprehensive guide on how to apply the causal models in automotive software engineering. We apply Bayesian propensity score matching for producing balanced control and treatment groups when we do not have access to the entire user base, Bayesian regression discontinuity design for identifying covariate dependent treatment assignments and the local treatment effect, and Bayesian difference-in-differences for causal inference of treatment effect overtime and implicitly control unobserved confounding factors. Each one of the demonstrative case has its grounds in practise, and is a scenario experienced when randomisation is not feasible. With the BOAT framework, we enable online software evaluation in the automotive domain without the need of a fully randomised experiment.