tokens: S = S t (and ). In Table 6 we present the statistical results of a linear least-squares analysis for the toy model ensemble, both prior to and after time-randomization, for , 0.010, and 0.020. These results can be compared directly against the results from Section 4 and Table 4 . As can be seen in the table, for a large value of there is a significant difference in the width of the measured slope histogram between the original time-ordered data and the randomized data, with the distribution of the original time-ordered data being significantly broader than that of the randomized data. In all three model cases, the width of the measured slope for the randomized data remains similar to that for both the time-ordered and randomized data obtained by the JCMT Transient Survey to date, suggesting that the uncertainty assumptions of the toy model are reasonable. As the magnitude of decreases, the measured slope distribution for the time-ordered data becomes narrower. The trends seen here are entirely as expected since the strength of the input slope within the toy model is proportional to and becomes directly measurable in the time-ordered data as the secular signal becomes greater than the uncertainty in the individual measurements. For the randomized data, the input slope is significantly disrupted and thus there is little signal remaining to influence the histogram. The observed trend is similar for the histograms of measured slope in units of the measured slope uncertainty. For large values of this width becomes significantly larger than unity for the time-ordered observations while the randomized distribution remains close to 1.1 (which is also the value obtained by the Transient Survey ensemble). Table 6 Secular Variability Analysis: Histogram Widths in the Toy Model Notes. a Standard deviation of S measured for all members of the ensemble (see the text). b Standard deviation of measured for all members of the ensemble (see the text). The toy model can be extended in order to predict the detection power of the JCMT Transient Survey after its full three years of observation. By increasing the number of observations to 30 and the time period to three years, we show in Table 6 that the difference in ensemble histogram widths between the time-ordered and random observations becomes much stronger for each value of . We thus conclude that at present we can rule out a Gaussian distribution of secular variations linear in time with but that a distribution with would be undetectable today. After the full three years of the survey, we expect to either measure or rule out distributions with . In each of these toy models, the normal distribution of linear slopes prevents there being a significant population of sources with large brightness variations, such as those observed by the JCMT Transient Survey (Table 5 ). This suggests that the five observed sources are indeed rare, statistical outliers. It should be recognized, however, that the toy models are
ner_tags: O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey O O O O O O O O O O O O O O O O O O O O O O O O O