Detecting Genetic Interactions for Quantitative Traits Using -Spacing Entropy Measure

Figure 2

The -independence and constant offset from the true value of the estimates averaged over all possible values for each . Each symbol represents a result of samplings from . While varying , the number of samples, the estimated entropy values were averaged over all the possible , sample-spacing values. denotes this averaging, which should not depend on weighting due to the virtually same standard deviations shown in Figure 1(b). Over a wide range of , the estimated entropy stays effectively the same, showing -independence in the range of practical number of sampling. Moreover, the almost flat line connecting each symbol shifts up or down following exactly the change of the true value indicated by the horizontal arrows. The rise in the extremely small range should be within the tolerable error of any specific application, because the contribution to conditional entropy by such a case would be suppressed by weighting, based on the marginal probability that should be proportional to .