The sufficient statistic from a regression study in econometrics is the least squares estimator x = (1.1, 0.3, -0.4, 2.2)', which can be considered to be an observation from a №(0, 0.314) distribution. Economic theory suggests that 01-021, and 03 =-1. These linear restrictions are felt to hold with accuracies of 0.3 and 0.5, respectively. (Consider these standard deviations.) A priori, nothing is known about 94, and there is thought to be no relationship between 01-02 and 03.

(a) Find the posterior mean and covariance matrix for 0, using the relevant robust prior from Section 4.7.10.

(b) Determine an approximate 95% credible ellipsoid for 0.