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On Bayesian learning from Bernoulli observations
Pier Giovanni Bissiri, Stephen G. Walker · 2009-02-17 · via math.ST updates on arXiv.org

We provide a reason for Bayesian updating, in the Bernoulli case, even when it is assumed that observations are independent and identically distributed with a fixed but unknown parameter $θ_0$. The motivation relies on the use of loss functions and asymptotics. Such a justification is important due to the recent interest and focus on Bayesian consistency which indeed assumes that the observations are independent and identically distributed rather than being conditionally independent with joint distribution depending on the choice of prior.

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