  In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal
detection techniques for gravitational wave detectors whose noise probability
distributions contain non-Gaussian tails. The methods modify standard methods
by truncating sample values which lie in those non-Gaussian tails. The methods
were derived, in the frequentist framework, by minimizing false alarm
probabilities at fixed false detection probability in weak signal limit. For
stochastic signals, the resulting statistic consisted of a sum of an
auto-correlation term and a cross-correlation term; it was necessary to discard
by hand the auto-correlation term to obtain the correct, generalized
cross-correlation statistic. In the present paper, we present an alternative
Bayesian derivation of the same signal detection techniques. We compute the
probability that a signal is present in the data, in the limit where the
signal-to-noise ratio squared per frequency bin is small, where the integrated
signal-to-noise ratio is large compared to one, and where the total probability
in the non-Gaussian tail part of the noise distribution is small. We show that,
for each model considered, the resulting probability is to a good approximation
a monotonic function of the detection statistic derived in the previous paper.
Moreover, for stochastic signals, the new Bayesian derivation automatically
eliminates the problematic auto-correlation term.
