What is Bayesian inference according to Press?
Bayesian inference is a principled framework for updating our beliefs in the face of new evidence. It formally incorporates prior knowledge or expectations about a parameter before observing data. Then, using Bayes' theorem, we combine this prior with the likelihood of the data given the parameter to arrive at a posterior probability distribution. This posterior represents our updated understanding, acknowledging both what we knew beforehand and what the data tells us. It's about quantifying uncertainty rigorously.
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