Applied Bayesian Modelling - Free

EXERCISES 3214. In Example 7.3, fit the ICAR(1) model including unstructured as well as spatialerrors and under the options with and without the AFF variable. How does the ratioof marginal variances (spatial to unstructured variances) change?5. Fit the Leyland et al. spatial model (see Example 7.4) to the lip cancer data ofExample 7.3. How does this affect the coefficient for the occupation variable?6. The following are 400 microwave backscatter measures in a large field in EastAnglia, UK, on a 20 20 grid with 12 m intervals between points:22 39 38 67 46 1 46 73 95 51 92 68 33 64 77 73 82 54 61 9743 36 58 32 35 35 88 56 73 64 74 62 55 73 105 80 90 21 57 10045 15 34 28 35 89 113 45 54 44 49 59 94 58 85 112 77 83 48 7548 14 14 83 55 81 73 33 58 74 81 78 66 96 69 102 94 86 96 8018 24 51 88 65 41 47 20 46 94 76 97 73 94 41 95 100 62 101 7566 53 40 50 29 19 67 50 57 85 57 88 69 106 88 79 98 69 82 95113 50 24 11 50 64 90 80 63 68 52 68 79 90 74 40 73 87 100 86103 31 45 29 56 115 132 78 82 54 70 51 40 69 80 71 88 95 94 6883 70 104 81 85 120 186 87 85 86 34 30 49 61 103 99 94 87 90 10472 78 186 132 111 153 157 119 90 82 80 95 79 57 79 57 68 105 63 9982 164 157 138 136 155 157 109 90 104 115 101 86 36 98 66 57 73 94 97107 166 157 101 101 93 157 85 82 80 111 82 77 104 67 70 79 57 76 81105 87 103 64 58 77 97 87 81 65 85 83 44 97 67 98 99 50 83 81145 116 91 94 34 49 73 64 46 83 60 69 90 89 63 89 84 67 47 86135 100 115 100 46 44 81 51 27 81 81 62 95 96 67 82 77 68 79 8078 127 115 90 47 92 103 79 58 95 54 70 93 105 68 100 39 65 98 9676 140 100 95 63 78 98 83 66 56 79 71 92 85 87 92 97 74 102 7882 119 69 83 78 40 73 81 77 93 61 63 78 62 87 61 76 75 98 2377 53 58 79 64 83 66 64 94 89 24 72 90 68 55 82 92 81 63 6486 63 78 84 67 78 63 71 91 60 80 54 80 98 65 80 99 61 73 37Group the 400.399=2 pairs of points into bands according to separations 0±12,12±24,. . . etc. up to a maximum distance band, and derive the necessary statistics for avariogram (this may be easier done outside BUGS). Then fit exponential andspherical variograms to the series, as in Example 7.5.6. In Example 7.7, compare the fit of the two models using the DIC criterion. How doesthis compare to the Gelfand±Ghosh criterion? Employing both criteria, fit a modelwhere a ij is a power function, namely a ij ˆ dij k .7. In Example 7.8, add code to find which areas have the maximum coefficients underthe GWR model. How does this add to knowledge about possible outlier areas? Also,consider the effect of taking Student t errors with known degrees of freedom (e.g.n ˆ 4).8. In Example 7.9, combine the heteroscedastic error model with an ICAR(r) spatialerror. How does this affect the AFF coefficient and the fit via DIC?9. In Example 7.11, fit the three parameter decay and direction functionwith a positive.f (d, u) ˆ [1 Z exp {b cos (u)}=d a ]