Monthly Archives: April 2026

Problem: State and prove Tweedie’s formula. Solution: Tweedie’s formula asserts that if \(p(\mathbf x|\boldsymbol{\mu},\sigma)=\frac{1}{\det(\sqrt{2\pi}\sigma)}e^{-(\mathbf x-\boldsymbol{\mu})^T\sigma^{-2}(\mathbf x-\boldsymbol{\mu})/2}\) is normally distributed, then without needing to know anything about the prior \(p(\boldsymbol{\mu}|\sigma)\) on the mean random vector \(\boldsymbol{\mu}\), one has the following Bayesian … Continue reading →