SWSN SCIENTIFIC REVIEW SERIES SWSN-SCI/ORP-2035-04-R3
3 Cross-domain residual coherence
3.1 Residual representation
For monitoring channelk, letyk(t) denote the observed quantity andˆyk(t|Mk) the prediction
from the accepted domain modelMk. We define a standardized residual
rk(t) = yk(t) − ˆyk(t|Mk)
ˆσk(t) . (1)
The working shared-factor model is
rk(t) = akz(t − τk) + ϵk(t), (2)
where z(t) is a latent process,ak is channel response,τk is a small lag andϵk is channel-specific
noise. This equation is intentionally agnostic about physical cause.
3.2 Reproducibility stress test
To verify the analysis pipeline before restricted data are reprocessed, we generated a 108-
month five-channel stress-test set containing an autoregressive latent process, three broad
transients, channel-specific lags and independent Gaussian noise. The code and exact seed
are preserved in the technical supplement. Figure1 shows the standardized series. The
point of this exercise is computational reproducibility, not empirical proof.
Figure 1:Normalized cross-domain residual stress-test series. Curves are vertically offset for visibil-
ity. Dashed lower trace is the latent reference used only for validation.
A principal-component analysis yields a first-component explained variance fraction of 0.6005.
A one-factor Gaussian model yields BIC= 1379 .4, compared with1555.9 for a diagonal Gaus-
sian null, giving∆BIC = 176 .5 in favor of shared covariance in this controlled stress test.
Figure 2 shows the residual correlation structure.
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