Consider the statistical linear model Y = A0+ € with m = 6 obser- vations, a parameter vector 0 = (01, 02, 03) with n = 3 components and €~ N(0; 200²16) having mean 0 and component variance 200². A realisation of this model for data Y and design matrix A is given by 580.8 -140.2 219.0 -64.5 73.4 403.8 = 87 1 2 3 1 734 635 2 15 573 0₁ 02 03 + €1 €3 EA €5 €6 (a) Find the Maximum Likelihood (ML) estimate of and the co- variance matrix Cov() of the ML estimate (b) If has prior distribution ~ N(0, 10213), then find the distribu- tion of posterior (0Y) using ridge regression. (c) Show that the component correlations Corr((0; Y), (0, Y)) of (0Y) are smaller than those of Corr(,) of the ML estimate for i ‡j.
Consider the statistical linear model Y = A0+ € with m = 6 obser- vations, a parameter vector 0 = (01, 02, 03) with n = 3 components and €~ N(0; 200²16) having mean 0 and component variance 200². A realisation of this model for data Y and design matrix A is given by 580.8 -140.2 219.0 -64.5 73.4 403.8 = 87 1 2 3 1 734 635 2 15 573 0₁ 02 03 + €1 €3 EA €5 €6 (a) Find the Maximum Likelihood (ML) estimate of and the co- variance matrix Cov() of the ML estimate (b) If has prior distribution ~ N(0, 10213), then find the distribu- tion of posterior (0Y) using ridge regression. (c) Show that the component correlations Corr((0; Y), (0, Y)) of (0Y) are smaller than those of Corr(,) of the ML estimate for i ‡j.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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