For the EEG data discussed in Section 2.3, perform the AR(8) Bayesian reference analysis as described there.

(a) Draw histograms of the marginal posterior distributions of the model coe cients j for j = 1 : 8

(b) Draw histograms of the marginal posterior distributions of the moduli and wavelengths of the complex reciprocal roots ordered by decreasing wavelength. In addition, compute a 95% posterior probability interval for each of these moduli and wavelengths.

(c) According to this analysis, what is the approximate posterior proba bility that the process is nonstationary?

(d) Obtain samples for some of the model error terms and draw his tograms of these samples. What is your assessment about the under lying normality assumption?

(e) Repeat the analysis described in Example 2.7 that keeps 2 AR compo nents and inverts the remaining 6 components. Compare your results with Figure 2.13.