  In this paper, we discuss a class of distributed detection algorithms which
can be viewed as implementations of Bayes' law in distributed settings. Some of
the algorithms are proposed in the literature most recently, and others are
first developed in this paper. The common feature of these algorithms is that
they all combine (i) certain kinds of consensus protocols with (ii) Bayesian
updates. They are different mainly in the aspect of the type of consensus
protocol and the order of the two operations. After discussing their
similarities and differences, we compare these distributed algorithms by
numerical examples. We focus on the rate at which these algorithms detect the
underlying true state of an object. We find that (a) The algorithms with
consensus via geometric average is more efficient than that via arithmetic
average; (b) The order of consensus aggregation and Bayesian update does not
apparently influence the performance of the algorithms; (c) The existence of
communication delay dramatically slows down the rate of convergence; (d) More
communication between agents with different signal structures improves the rate
of convergence.
