Based on the Bayesian spline estimation designed by Ogata et al., the spatiotemporal evolution of b-values was achieved through Delaunay triangulation and penalty constraints.
A method of connecting a given set of points on a plane into triangles, such that the resulting triangles have the following properties:
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The triangles do not overlap each other.
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The triangles collectively cover the entire plane.
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No point lies inside the circumcircle of any triangle that does not contain it (i.e., within the circumcircle of a triangle, only the three vertices on the circle are included, and no other points).
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The Delaunay triangulation maximizes the minimum angle among all triangles formed by connecting a given set of points
# [Now] Weight Penalty ABIC ABIC-like Loglik Iter
# [1/16] 1.000e-03 5.362 2374.620 663.315 -325.296 7
# [2/16] 2.512e-03 6.797 2088.063 674.405 -329.406 4
# [3/16] 6.310e-03 9.568 1819.906 689.187 -334.025 3
# [4/16] 1.585e-02 14.286 1578.944 710.897 -340.163 4
# [5/16] 3.981e-02 19.545 1376.028 742.178 -350.544 4
# [6/16] 1.000e-01 23.138 1219.601 781.827 -366.776 4
# [7/16] 2.512e-01 24.439 1111.320 825.999 -387.561 4
# [8/16] 6.310e-01 23.740 1046.347 870.630 -410.575 3
# [9/16] 1.585e+00 21.485 1015.214 912.513 -433.772 3
# [10/16] 3.981e+00 18.002 1006.327 949.005 -455.500 3
# [11/16] 1.000e+01 14.130 1009.329 978.622 -474.181 3
# [12/16] 2.512e+01 10.058 1016.774 1000.933 -489.408 3
# [13/16] 6.310e+01 6.127 1023.696 1015.749 -500.748 3
# [14/16] 1.585e+02 3.186 1028.133 1024.131 -507.880 3
# [15/16] 3.981e+02 1.472 1030.415 1028.252 -511.654 3
# [16/16] 1.000e+03 0.631 1031.450 1030.090 -513.414 3
# =====================================
# Spatial b-value fitting finished
# Number of events=2000
# Number of vertices=900
# Number of triangles=1682
# Constant b-value=0.91
# Best W=3.98
# Best ABIC=1006.327
# Best Loglik=-455.500
# Best Roughness=4.522
# =====================================
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