  The problem of large scale multiple testing arises in many contexts,
including testing for pairwise interaction among large numbers of neurons. With
advances in technologies, it has become common to record from hundreds of
neurons simultaneously, and this number is growing quickly, so that the number
of pairwise tests can be very large. It is important to control the rate at
which false positives occur. In addition, there is sometimes information that
affects the probability of a positive result for any given pair. In the case of
neurons, they are more likely to have correlated activity when they are close
together, and when they respond similarly to various stimuli. Recently a method
was developed to control false positives when covariate information, such as
distances between pairs of neurons, is available. This method, however, relies
on computationally-intensive Markov Chain Monte Carlo (MCMC). Here we develop
an alternative, based on Sequential Monte Carlo, which scales well with the
size of the dataset. This scheme considers data items sequentially, with
relevant probabilities being updated at each step. Simulation experiments
demonstrate that the proposed algorithm delivers results as accurately as the
previous MCMC method with only a single pass through the data. We illustrate
the method by using it to analyze neural recordings from extrastriate cortex in
a macaque monkey.
