Based on over fifty years’ experience of applying Bayesian methodology in statistical, risk and decision analyses, I reflect on its power in supporting sound scientific induction. I argue that Bayesian methods are more suited to guiding inferences than other methods. In the past, Bayesians justified their approach through its rigorous axiomatic base and its intuitive good sense in modelling rational inference. Nowadays, the easily comprehended interface offered by belief nets, the computational power of MCMC to conduct complex analyses, and the general fit of Bayesian methodology with machine learning are more likely to be offered as justification. Here I offer a further perspective, focusing on the support Bayesian analysis offers scientific induction. Using Shafer’s interpretation of prescriptive analysis as ‘argument by analogy’, I argue that Bayesian analysis is better suited to nudging scientists towards rational inference in confirmatory studies and reducing the risk that they may be misled by subconscious biases. However, I also recognise that non-Bayesian approaches can be very useful in exploratory analyses. Moreover, I recognise that subjective probabilities cannot model all the uncertainties that must be addressed in sound scientific induction. The unmodelled ones, I suggest, need much more recognition and attention than apparent in current practice. Throughout, I recognise that the process of scientific induction is – or ideally would be – driven by a series of interactions between scientists and statisticians. Thus the paper presents my personal perspective on how a subjective statistician should engage with scientists to support their scientific induction.
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