Statistics Graduate Level Quiz
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ADVANCED TOPICS IN GRADUATE STATISTICS
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Consider the Gaussian model y∣β∼N(Xβ,σ2I)y\mid β\sim N(Xβ,\sigma^2I), with the intercept treated separately. Ridge is defined by minimizing 12∣∣y−Xβ∣∣22+λ2∣∣β∣∣22\frac{1}{2}||y-Xβ||_2^2+\frac{\lambda}{2}||β||_2^2, and lasso by minimizing 12∣∣y−Xβ∣∣22+λ∣∣β∣∣1\frac{1}{2}||y-Xβ||_2^2+\lambda||β||_1.
Which prior specifications produce these estimators as posterior modes with the stated values of λ\lambda?
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