  Observational astronomy in the time-domain era faces several new challenges.
One of them is the efficient use of observations obtained at multiple epochs.
The work presented here addresses faint object detection with multi-epoch data,
and describes an incremental strategy for separating real objects from
artifacts in ongoing surveys, in situations where the single-epoch data are
summaries of the full image data, such as single-epoch catalogs of flux and
direction estimates for candidate sources. The basic idea is to produce
low-threshold single-epoch catalogs, and use a probabilistic approach to
accumulate catalog information across epochs; this is in contrast to more
conventional strategies based on co-added or stacked image data across all
epochs. We adopt a Bayesian approach, addressing object detection by
calculating the marginal likelihoods for hypotheses asserting there is no
object, or one object, in a small image patch containing at most one cataloged
source at each epoch. The object-present hypothesis interprets the sources in a
patch at different epochs as arising from a genuine object; the no-object
(noise) hypothesis interprets candidate sources as spurious, arising from noise
peaks. We study the detection probability for constant-flux objects in a
simplified Gaussian noise setting, comparing results based on single exposures
and stacked exposures to results based on a series of single-epoch catalog
summaries. Computing the detection probability based on catalog data amounts to
generalized cross-matching: it is the product of a factor accounting for
matching of the estimated fluxes of candidate sources, and a factor accounting
for matching of their estimated directions. We find that probabilistic fusion
of multi-epoch catalog information can detect sources with only modest
sacrifice in sensitivity and selectivity compared to stacking.
