  We present algorithms for searching for azimuthally symmetric features in CMB
data. Our algorithms are fully optimal for masked all-sky data with
inhomogeneous noise, computationally fast, simple to implement, and make no
approximations. We show how to implement the optimal analysis in both Bayesian
and frequentist cases. In the Bayesian case, our algorithm for evaluating the
posterior likelihood is so fast that we can do a brute-force search over
parameter space, rather than using a Monte Carlo Markov chain. Our motivating
example is searching for bubble collisions, a pre-inflationary signal which can
be generated if multiple tunneling events occur in an eternally inflating
spacetime, but our algorithms are general and should be useful in other
contexts.
