2 also affect robustness. In some methods, prior informa- tion is used about generic features of the function to be maximized. This may not be reliable if the assumptions behind the prior information, such as a particular noise model, become invalid. To properly address issues such as these it is important that a wide variety of stochastic methods be explored in GW data analysis . Particle Swarm Optimization (PSO) [11], first pro- posed by Kennedy and Eberhardt in 1995, is a stochas- tic method that has been garnering a lot of attention recently in many application areas [12]. An attractive feature of PSO is that, in its basic form, it has a small number of design variables. On standard testbeds, PSO has been found to have comparable or superior perfor- mance to other well known methods such as MCMC. This paper presents the first application of PSO to GW data analysis. We pose the following specific questions: 1. Is PSO a viable method when applied to a function that is highly multi-modal and essentially stochas- tic in nature? This is the typical case in GW data analysis. 2. How many design variables are there in PSO, and how many of them need to be tuned well? 3. Can the tuning of these variables be done with- out requiring prior information about features of the function, thus increasing the robustness of the method? 4. What is the computational cost of the method and what are the most important technical improve- ments required for the future? To answer these questions in the most direct and reliable manner, we construct a testbed based on the well un- derstood task of detecting and estimating binary inspiral signals in data from a single ground-based detector. This problem involves low-dimensionality but offers the more serious challenge of high multi-modality. To keep the fo- cus on the latter, a simplification is made regarding the shape of the search region such that it admits unphysical waveforms. Thus, the implementation of PSO presented here is not directly applicable to binary inspiral searches at present. The required technical refinements are dis- cussed in the paper. In addition, a novel and system- atic tuning procedure is introduced that is based on data containing only noise. This procedure may be useful for other stochastic methods also. The rest of the paper is organized as follows. Sec. II describes the testbed and Sec. III describes the PSO method. We explain our procedure for tuning the de- sign variables of PSO in Sec. IV. Sec. V then presents results from numerical simulations. Our conclusions and pointers to future work are presented in Sec VI. A. Noise model II. TEST BED Notation x , y , etc: A time series with a finite number, N , of A GW signal incident on an interferometric ground- based detector produces a difference in the lengths of its two arms. After calibrating out the common arm length and the transfer function of the detector, the data, x , In this section, we describe the testbed to which PSO is applied. The testbed is constituted by the noise model, signal family and the function to be maximized. induced by the inner product defined above. The signal to noise ratio (SNR) of a signal s (Θ) is de- fined as ‖ s (Θ) ‖ . where S$_{n}$ [ k ] is the one-sided Power Spectral Density (PSD) of the noise. ‖ y ‖ : the norm on R $^{N}$, ‖ y ‖ 2 = 〈 y , y 〉 , (2) 〈 x , y 〉 = 4 R  $^{[}$$^{N/}$$^{2+1]}$ ∑ k =0 ˜ x $^{∗}$[ k $^{]}$˜ y [ k ] S$_{n}$ [ k ] T   (1) frequency by ˜ s [ k ; Θ]. x , y 〉 : The time series introduced above are elements of R $^{N}$, the vector space of real N -tuples. From the point of view of detection and estimation of a signal in data with additive stationary noise, a natural inner product can be introduced on this vector space, ˜ x : The Discrete Fourier Transform (DFT) of x . The DFT value at the frequency k/T , k = 0 , 1 , . . . , [ N/ 2 + 1], is denoted as ˜ x [ k ]. The DFT of s (Θ) is denoted by ˜ s (Θ) and its value at the k th frequency by s [ k ; Θ]. 〈 x , y 〉 : The time series introduced above are elements s (Θ): The time series of the signal corresponding to parameter values Θ. The k th sample of s (Θ) is denoted by s [ k ; Θ]. In our case, signals have a well-defined start and stop time and the interval between them may be less than T . However, s (Θ) still consists of N samples with the samples outside the interval enclosed by the start and stop times set to 0 (zero-padding). Θ : The set of parameters describing a family of signals. δ$_{s}$ , T : The sampling interval and the duration of x re- spectively. The number of samples in x is N = [ T/δ$_{s}$ ], where the square brackets denote trunca- tion to the nearest integer. samples. The k th sample, 0 ≤ k ≤ N − 1, is denoted by x [ k ].