6 N$_{rep}$ : For given data x , independent runs of PSO yield different values of λ ( θ | x ) corresponding to the dif- ferent fitness values at termination. This is un- avoidable for any stochastic method. However, ter- mination near the true global maximum in indepen- dent runs of PSO on the same data should result in the clustering of the different values found and their locations. We can turn this argument around by running PSO independently several times on the same data and using the formation of a cluster as an indicator of successful termination in the vicinity of the global maximum. The number of independent runs of PSO on the same data, N$_{rep}$ , is also a design variable. is to provide a testbed for PSO, this physical constraint is ignored. The rectangular search region allows the coordinate transformation, x$_{1}$ = ( τ$_{0}$ − τ$_{0}$$_{,min}$ ) / ( τ$_{0}$$_{,max}$ − τ$_{0}$$_{,min}$ ) , (14) x$_{2}$ = ( τ$_{1}$$_{.}$$_{5}$ − τ$_{1}$$_{.}$$_{5}$$_{,min}$ ) / ( τ$_{1}$$_{.}$$_{5}$$_{,max}$ − τ$_{1}$$_{.}$$_{5}$$_{,min}$ ) , (15) such that x$_{i}$ ∈ [0 , 1], i = 1 , 2. In our codes, all PSO equations use x$_{1}$ and x$_{2}$ and the corresponding velocity components. We choose τ$_{0}$$_{,min}$ = 0 . 94 sec, τ$_{0}$$_{,max}$ = 37 . 48 sec, τ$_{1}$$_{.}$$_{5}$$_{,min}$ = 0 . 234 sec and τ$_{1}$$_{.}$$_{5}$$_{,max}$ = 1 . 021 sec. With τ$_{0}$ and τ$_{1}$$_{.}$$_{5}$ along the horizontal and vertical axes respec- tively, the upper right hand corner corresponds to binary component masses (in M$_{⊙}$ ) m$_{1}$ = 1 . 1 and m$_{2}$ = 1 . 1. The lower left hand corner corresponds to m$_{1}$ = 10 . 5 and m$_{2}$ = 9 . 7. For any stochastic method, convergence to the global maximum can only be quantified as a probability. In some asymptotic limit, such as particle number N$_{p}$ → ∞ for PSO, this probability becomes unity. However, this also implies an infinitely large computing cost. Thus the design variables must be tuned to find the best trade-off between the probability of convergence and the associ- ated computational cost. We present here the procedure followed for tuning the design variables of PSO. In contrast to the tuning procedure used for most MCMC methods in the GW literature, our approach is not based on data containing a signal but data that is purely noise. The latter is the worst case scenario for any stochastic method. However, good performance in the pure noise case more or less guarantees success when a signal is present. Moreover, this approach to tuning avoids any bias due to the use of a particular set of sig- nals or SNRs. The tuning procedure presented here can be used, in principle, to tune all the nine design variables of PSO (c.f., Sec. III D). However, applying the procedure to all of them is computationally too expensive, at least for the objectives of this paper. We focus instead on two of the most important variables for the performance of PSO, N$_{p}$ and N$_{t}$ . For the rest, we either choose values commonly used in the literature or simply pick reasonable ones based on our experience with PSO. Thus, we set : c$_{1}$ = c$_{2}$ = 2, V$_{max}$ = (0 . 5 , 0 . 5), w$_{0}$ = 0 . 9, m = 0 . 4, α = 0 . 03 and N$_{rep}$ = 5. A. Criterion for optimal tuning IV. TUNING THE DESIGN VARIABLES D. PSO design variables One of the questions posed at the beginning was about the number of design variables in PSO. In our implemen- tation, there are a total of 9 that are listed below for reference. N$_{p}$ : Number of particles in the swarm. c$_{1}$, c$_{2}$ : Acceleration constants. V$_{max}$ : Maximum velocity of a particle. Parameters governing the inertia decay law: The iner- tia weight is decreased in value as PSO progresses through a search. The PSO literature is full of different types of decay laws but, in general, it is known that a strictly linear decay law is not very useful. We have developed the following de- cay law that has elements of both linearity and non- linearity. Let w [ k ] be the value of the inertia weight at step k , α, N$_{t}$ : The parameters used to specify the termination criterion for PSO. These parameters are not part of the standard PSO algorithm. w [ k ] = w$_{0}$ − m ( k − k$_{0}$ ) /N$_{t}$ , (16) Measuring the probability of convergence for the pure noise case presents a practical problem. In simulations where a large SNR signal is present, we know that the true maximum is most likely to be in close proximity to the location of the signal and it can be found reliably using, say, a small area grid-based search. For the pure noise case, however, the location is not known a priori , where w$_{0}$ > 0 and m > 0. The parameter k$_{0}$ starts with an initial value of k$_{0}$ = 0 and is kept fixed as long as gbest stays within the current region of convergence. If gbest exits the convergence region at some step k ′ without termination, k$_{0}$ is set equal to k $^{′}$. Thus, the value of the inertia is reset to the starting value of w$_{0}$ every time termination fails and the linear decay of the inertia starts anew.