As mentioned above, we use three indices, the correlation coefficient and two kinds of variance reductions, to compare (O({varvec{r}}_i, t)) to (C({varvec{r}}_i, t)).
The three indices are a correlation coefficient and two kinds of variance reductions and are used to compare the observed waveforms and the pre-calculated waveforms in the TSB.
These examinations enabled us to confirm that appropriate tsunami scenarios could be selected by using the three indices, which consist of two kinds of variance reductions and a correlation coefficient, with offshore waveforms obtained by both pseudo-observation and by calculation, both of which are derived from ocean-bottom pressure changes.
Mathematical considerations and synthetic examinations revealed that two different kinds of variance reductions, (hbox {VRO}(t)) and (hbox {VRC}(t)), which are normalized by the L2-norm of either the observed or calculated waveforms, are sensitive to overestimation or underestimation of the tsunami size.
We apply three indices, which are the correlation coefficient and two kinds of variance reductions normalized by the L2-norm of either the observation or calculation, to match the observed spatial distributions with the pre-calculated spatial distributions in the TSB.
Based on the test results, we confirm that the method can select appropriate tsunami scenarios within a certain precision by using the two kinds of variance reductions, which are sensitive to the tsunami size, and the correlation coefficient, which is sensitive to the tsunami source location.
Sleep staging by a human rater or by supervised programs can absorb many kinds of variance in the EEG/EMG data although it sacrifices the objectivity because of inter- or inner-rater differences.
In this kind of analysis, the variance of each dependent variable is partitioned into components due to different factors in order to see if the variability observed in the dependent variable is due to variations in factors or results from "by-chance" effects.
