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Normal Approximation to the Posterior Distribution | Bounded Rationality

bjlkeng.github.io · 3,323 words · saved by 1 readers

A brief note on using a normal distribution to approximate a Bayesian posterior distribution.

In this post, I'm going to write about how the ever versatile normal distribution can be used to approximate a Bayesian posterior distribution. Unlike some other normal approximations, this is not a direct application of the central limit theorem. The result has a straight forward proof using Laplace's Method whose main ideas I will attempt to present. I'll also simulate a simple scenario to see how it works in practice. Background ¶ We're going to first start by reviewing some simple terminology and definitions regarding Bayesian methods to make the discussion later a bit easier to follow. Th

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