Consider a linear regression model from x 2 Rn to y 2 R: y = w|x + ", where w 2 Rn is the model parameter, and " is an independent zero-mean Gaussian noise "  N

????

0, 2

. Assume we choose a Gaussian distribution as the prior of the model parameter w: p¹wº = N

????

w0, 0

. Assuming we have obtained the training set D =



¹x1, y1º, ¹x2, y2º,


, ¹xN, yNº

, derive the posterior distribution p¹wjDº, and give the MAP estimation of the model parameter wMAP.