The comparison of the precisions estimates of (a) covariance and (b) coincidence for covariances ranging from three orders of magnitude below the noise terms to three orders of magnitude above the noise. The noise terms have been set to 1. In all cases the precision of the covariance is better than that of the coincidence.
Scaling of the resolving time shows how covariance can extract correlated signal even when accidental coincidences overwhelm correlated coincidences. Curve (a) is the coincidence signal. Curve (b) is the estimated accidental coincidence contribution, and curve (c) is the covariance. On these time scales the correlated signal is constant, so the true coincidence curve, represented by the covariance, should remain flat.
The positive covariances in this map show correlations between cascade gammas emitted after the radioactive decay 133Ba. Such correlations are nuclide specific and can serve as secondary spectral signatures.
Negative covariances in this map shows competing pathways in the relaxation of the 133Cs daughter nucleus from radioactive decay of 133Ba. These features can also be exploited for spectral identification. This map was generated from the same data that produced the map shown in Fig. 3 .
This covariance map shows three islands of covariance in the vicinity of 1.3 MeV. The data are from a 60Co source masked by a stronger 22Na source. The average spectra show only two peaks, but the covariance map can resolve three. The features marked (a) and (b) are from the 60Co correlated cascade gammas at 1.17 MeV and 1.33 MeV. The feature marked (c) is the 22Na correlation between 511 keV and 1.27 MeV.
This covariance map is for stand-off detection by a NaI detector array of a 60Co source. No covariance features from source correlations are visible, and all the features seen here are from detector crosstalk. Compton reconstruction of this covariance table produces the spectrum shown in Fig. 7 .
Spectral reconstruction of Compton crosstalk is accomplished by cross diagonal summing of the covariance table. Curve (a) is reconstructed spectra from the Compton continuum by processing the covariance table for the data of Fig. 6 . Shown for comparison, the curve labeled (b) is the average spectra. Reconstruction of the Compton continuum of these data yields 50% extra photo peak signal.
The covariance filtered (a) background spectrum from an array of HPGe detectors shows peaks that are correlated with the 511 keV gamma peak from pair production. Single and double escape peaks of 209Tl are located at 2103 keV and 1592 keV, and the single escape peak of 40K is visible at 950 keV. The negative covariance at 1460 keV indicates an anti-correlation between pair production and the full energy photo peak of 40K. For reference, the average spectrum (b) is plotted scaled and offset above the filtered spectrum.
Fourfold table of probabilities for detection of the latent variable A.
First four raw and central moments for a Poisson distribution.
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