Intro to Bayes Approach. Reasons to Be Bayesian Differences between Bayesian and Frequentist Approaches

Abstract

Differences between Bayesian and Frequentist Approaches Frequentist • θ is fixed, but unknown • Uncertainty comes from sampling uncertainty. That is, from the fact that we can get different samples. • All probabilistic statements are statements about sampling uncertainty. For example, ˆ – Eθθ(YT ) = θ (unbiasedness) means in average over all possible repeated samples, one receives the true value – Pθ{θ ∈ C(YT )} = 1 − α coverage probability of confidence sets is a statement about the ratio (in repeated samples) of sets containing θ. Once we observe a sample, θ is either in the set or not; there is no probability, after realization of a sample. The coverage probability is a statement about ex-ante probability.

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