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首先，Yes this is a crucial aspect of Bayesian statistics. Since the posterior directly depends on the prior, of course it has some effect. However, the more data you have, the more your posterior will be determined by the likelihood term. This is especially true if you take a “wide” prior (wide Gaussian, uniform, etc.) The reason for this is that the more data you have, the more structure (i.e. local peaks) your likelihood will have. When multiplying with the prior, these will barely be perturbed by the flat portions of the prior, and will remain features of the posterior. But when you have little data, the opposite happens, and your prior is more reflected in the posterior data. This is one of the strengths of Bayesian statistics. The prior is here to compensate for lack of data, and when sufficient data is present, it bows out.3
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