The final topic in measuring spatial autocorrelation is LISA or Local Indicators of Spatial Association.
All the previously discussed measures of spatial autocorrelation share the common weakness that they do not identify specific locations on a map where the measured autocorrelation is most pronounced. That is, they are global measures, which tell us that the map data are spatially autocorrelated but not where to find the data that contribute most to that conclusion. Equally, global measures do not allow us to identify map regions where the pattern runs counter to the overall spatial autocorrelation trend.
LISA statistics address these failings and exemplify a trend in spatial analysis in favor of approaches that emphasize local effects over global ones. (See the papers by Unwin 1996 and Fotheringham 1997 cited in the text for more details on this trend.)
The LISA approach simply involves recording the contributions from individual map units to the overall summary measure, whether it is Moran's I or any other measure.
Significance tests on LISA statistics are hard to calculate and generally depend on Monte Carlo simulation, which is discussed on page 84 and again on pages 89-90 of the text, and which you also encountered in Lesson 3's project. The idea is that a computer can randomly rearrange the map unit values many times, measuring the LISA statistic for each map unit each time, and then determine if actual observed LISA values are unusual with respect to this simulated distribution of values. There are some wrinkles to this, revolving around the challenges of multiple testing.