LIGO Document G0900562-v3

Random template placement and prior information

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In signal detection problems, one is usually faced with the task of searching a parameter space for peaks in the likelihood function, indicating the presence of a signal. Random searches have proven to be very efficient as well as easy to implement, compared e.g. to searches along regular grids in parameter space. Knowledge of the parameterised shape of the signal searched for adds structure to the parameter space, i.e., there are usually regions requiring to be densely searched while in other regions a coarser search is sufficient. On the other hand, the prior information identifies the regions in which a search will actually be promising or may likely be in vain. Defining specific figures of merit allows to join both template metric and prior distribution and achieve an optimal sampling in a certain sense. We show an example related to the gravitational wave signal from a binary inspiral event, where template metric and prior information are particularly contradictory, since low-mass systems allow the least mismatch in parameter space while high-mass systems are far more likely, as they imply a greater SNR and hence are detectable to greater distances.
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