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In this paper, we present a different perspective which focuses on missing observations as the source of statistical uncertainty, with the parameter of interest being known precisely given the entire population. We argue that the foundation of Bayesian inference is to assign a distribution on missing observations conditional on what has been observed. In the conditionally i.i.d. setting with an observed sample of size $n$, the Bayesian would thus assign a predictive distribution on the missing $Y_{n+1:\\infty}$ conditional on $Y_{1:n}$, which then induces a distribution on the parameter. Demonstrating an application of martingales, Doob shows that choosing the Bayesian predictive distribution returns the conventional posterior as the distribution of the parameter. Taking this as our cue, we relax the predictive machine, avoiding the need for the predictive to be derived solely from the usual prior to posterior to predictive density formula. 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