# Fixed-point method for validating the first-order approach plates,

If the events are clustered, then the G w values should be higher than the F x values. Point A Point B Tao is the bandwidth and determines resolution Edge corrections should be used if points are near the edge 6 Exploring point patterns Nearest neighbour distances: For linear and areal data there are also a similarly wide variety of methods, and once you get into GLMs you will encounter many sophisticated solutions.

Edge effects are problematic when working with theoretical distributions, so normally a computational intensive Monte Carlo approach is taken.

Edge effects can affect the results. If there is no interaction the plot should be roughly a straight line. Methods consider first-order effects e.

Heterogeneous Poisson process the intensity of the process varies across space [e. Therefore either use a guard region buffer around edge or a toroidal shift technique.

Use the observed events from one spatial process that are representative of the population variations the control process. Could plot k against h.

In order to determine the significance of the observed pattern, we randomly label the combined events into cases and controls. The mean values are determined for each distance class, as well as the min and max values observed within each class.

The theoretical values mean, min, max are plotted against the observed values.

If clustering is present the plot will lie above the line, if regularity the plot will lie below the line assuming the simulated values are plotted on the x-axis.

The K function is: Point A will count less than Point B. That is, CSR is not a viable option, since there is an expectation that there is some natural spatial variation in the intensity of the process e.

The is the most commonly assumed process. K functions are the preferred means to examine point patterns as they consider all scales not just the nearest neighboursand they have a theoretical basis.

If curve rises rapidly at beginning, suggests clustering of events, if rises late, suggests regularity. Similar presentations More Presentation on theme: This time, we plot L ii hL jj h and L ij h simultaneously, which reveals whether individually i or j depart from CSR, as well as if i and j appear to be attracted positive peaks or repulsed negative troughs in the plot.

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