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Good gawd, we need to uniformise the notation in the manuscript!
I personally strong dislike the p(theta | y) ~~ p(y | theta)p(theta) notation because it overloads the letter p with wildly different things. In my writing I usually use p(theta|y) for the posterior, Pr(A|y) for the probability of an event A conditional on the data, f(y|theta) for the likelihood and \pi(theta) for the prior.
Whatever we choose, we should be consistent with it.
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