The Why & How of X-Ray Timing - HEASARC - NASA

Statistics: Solutions• Average adjacentfrequency bins• Divide up data intosegments, make powerspectra, average them(essentially the samething)• Averaging M bins togetherresults in noise distributedas χ 2 /M with 2M d.o.f. for hypothesis testing,still chi-squared, but withmore d.o.f.• However, in detecting asource, you examine manyFourier bins, perhaps allof them. Thus, thesignificance must bereduced by the number oftrials. Confidence isC = 1 – N bins × Prob(MP j ,2M),where N bins is the numberof PDS bins (i.e., trials),and Prob(χ 2 ,ν) is thehypothesis test.