Calculate the overlap between two stationary distributions
This function calculates a useful measure of similarity between distributions known as the Bhattacharyya coefficient in statistics and simply the fidelity or overlap in quantum and statistical mechanics. It is roughly speaking the ratio of the intersection area to the average individual area. When applied to
ctmm objects, this function returns the overlap of the two Gaussian distributions. When applied to
telemetry or (aligned)
UD objects with corresponding movement models, this function returns the overlap of their (autocorrelated) kernel density estimates.
The confidence level desired for the output.
Additional arguments relevant for
A table of confidence intervals on the overlap estimate. A value of
1 implies that the two distributions are identical, while a value of
0 implies that the two distributions share no area in common.
ctmm objects are necessary to provide confidence intervals on the point esitmate.
CTMM2 are propagated into the overlap estimate under the approximation that the Bhattacharyya distance is a chi-square random variable.
C. H. Fleming and K. Winner
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# Load package and data library(ctmm) data(buffalo) # Fit a continuous-velocity model with tau ~ c(10 days,1 hour) # also see help(variogram.fit) GUESS <- ctmm(tau=c(10*24*60^2,60^2)) FITS <- list() FITS[] <- ctmm.fit(buffalo[],GUESS) FITS[] <- ctmm.fit(buffalo[],GUESS) names(FITS) <- names(buffalo[1:2]) # Gaussian overlap between these two buffalo overlap(FITS) # AKDE overlap between these two buffalo overlap(buffalo[1:2],FITS)
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