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Suppose we observe two datasets D1 and D2 sequentially, and assume that P(D1, D2 | theta) = P(D1 | theta) * P(D2 | theta). How

Suppose we observe two datasets D1 and D2 sequentially, and assume that P(D1, D2 | theta) = P(D1 | theta) * P(D2 | theta).

How do we prove that P(theta | D1, D2) is proportional to P(theta | D1) * P(D2 | theta), and what does this suggest about the sequential updating for Bayesian model?

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