Optimum Period Search: Quantitative Analysis

Statistical properties of two broad classes of methods used in period search, namely, phase binning and model function methods, are compared. We employ hypothesis-testing theory to study these methods and present closed analytical formulae for evaluation of the sensitivity of period search, for different kinds of signals. Based on this theory, we draw two conclusions: (1) the methods using smooth model functions are generally more sensitive than those using phase binning and (2) the resolution of the model functions should match structures in the detected signal. Both excess and insufficient resolution result in decreased detection sensitivity. Finally, we demonstrate that within the broad class of the methods discussed, methods utilizing the same models but different statistics generally are equally sensitive. Our considerations apply to most existing period-search methods, which enable formulation of statistical detection criteria.