Selection of bandwidth type and adjustment side in kernel density estimation over inhomogeneous backgrounds

Figures & data

Figure 1. An illustration of the fixed-bandwidth KDE versus the adaptive-bandwidth KDE over raster data.

Figure 2. An illustration of the site-side versus case-side calculations over raster data.

Figure 3. Site-side versus case-side: determining the contribution of a case to a site.

Figure 4. Case-side versus site-side: sensitivity to the spatial variation of population.

Figure 5. Population (expected count) of lung cancer cases in Merrimack County, NH.

Figure 6. Density of lung cancer cases in Merrimack County calculated using different kernel approaches: (a) fixed-bandwidth and site-side; (b) fixed-bandwidth and case-side; (c) adaptive-bandwidth and site-side; (d) adaptive-bandwidth and case-side.

Table 1. Calculation details of the example results

		Actual Bandwidth (m)				Actual Expected Count (Population)				Running
Approach		Min	Max	Mean	Std Dev	Min	Max	Mean	Std Dev	Time (Seconds)
Fixed-Bandwidth	Site-side	4999.3	4999.3	4999.3	0.0	0.4	196.4	22.1	29.3	1332
	Case-side	4999.3	4999.3	4999.3	0.0	1.2	190.9	71.1	60.5	6
Adaptive-Bandwidth	Site-side	495.0	18028.7	5669.0	2430.1	15	15.6	15	0.0	2522
	Case-side	502.5	12750.1	2744.4	2219.0	15	15.5	15	0.1	12

Figure 7. High-density areas (>mean  +  2 std dev) of lung cancer cases in Merrimack County identified by different kernel approaches: (a) fixed-bandwidth and site-side; (b) fixed-bandwidth and case-side; (c) adaptive-bandwidth and site-side; (d) adaptive-bandwidth and case-side.

Table 2. Correlation coefficients between the results from the four methods

	Site-side-fixed	Case-side-fixed	Site-side-adaptive	Case-side-adaptive
Site-side-fixed	1	0.94	0.73	0.65
Case-side-fixed	0.94	1	0.71	0.69
Site-side-adaptive	0.73	0.71	1	0.89
Case-side-adaptive	0.65	0.69	0.89	1