Fig. 1

a The simulation process to identify possible districts of origin (green, yellow, purple, and pink areas), for a hypothetical survey cluster from a Demographic and Health Survey. The maximum displacement area with a radius of two km in an urban area or five km in a rural area (black circle) surrounds the mapped sampling unit location (black dot). First, a distance is chosen (white solid arrow), and then, an angle is chosen, (white broken arrow). b This process is simulated 1000 times to estimate relative likelihoods for possible districts of origin. 200 simulations (white circles) are pictured, method A assigns all four districts non-zero probability proportions: 0.13, 0.24, 0.33, 0.29 (green, yellow, blue, and pink, respectively), while method B identifies the blue district, and method C identifies the yellow district as the district of origin