tokens: gives a power spectrum with the desired shape. We then inverse Fourier transform back to get the pink or red time stream. We then take samples with a positive value to contain a pulse and samples with a negative value to contain none. In the stationary Poisson case, the rate of bursts in the immediate follow-up is the same as the multiyear follow-up since all times are statistically equivalent. However, with flicker noise, the variance is strongly time dependent. If we imagine an object that repeated on average once per two hours, then if those pulses were Poisson-distributed, the probability of seeing zero bursts in 11.4 h or longer is ∼0.007. With pink noise, one expects this roughly 20 per cent of the time, since the system prefers either to be in ‘on’ or ‘off’ mode. If the average repeat period were more like 5–20 h, then we would often see nothing in a multiday follow-up observation that took place weeks or years after the initial event. This is consistent with what Petroff et al. ( 2015b ) saw, though the conclusions differ depending on the assumed statistics. In Fig. 1 , we show a sample from this simulation for three repeat distributions. The right-hand panel shows how, if an FRB's burst rate has long-term correlations (1/ f γ ), the likelihood of a repeat is greatly increased if the follow-up observation is immediately after the initial event, rather than months or years after. Figure 1. Realization of our mock follow-up Monte Carlo. Left-hand panel: power spectrum for pulse arrival times of a single FRB. Grey shows a flat spectrum, corresponding to the often assumed Poissonian repetition rate. The red and blue spectra show flicker noise, with pink (1/ f ) noise and Brownian (1/ f 2 ) noise, respectively. Right-hand panel: we found the first ‘event’ in our Monte Carlo (represented by a star) for the three different spectra and plotted their behaviour in the subsequent 48 h of follow-up. Though the average probability over the whole simulation is 0.5 for each distribution, when we zoom in on this short period, the strong time-like correlations in the 1/ f γ cases means there are many repetitions, they are in an ‘on’ state at this time. 2.2 FRBs 110220 and 140514 Using the event rate of roughly 10 4 sky −1 d −1 from Thornton ( 2013 ), it was originally reported that the probability of seeing a new FRB in the field of 110220 during the 85 h of follow-up was 0.32 (Petroff et al. 2015a ). It was then pointed out by Maoz et al. ( 2015 ) that this underestimated the coincidence by an order of magnitude, since they estimated the rate in any one of the 13 beams, while the new event occurred in the identical beam. The probability also dropped due to the updated daily event rate, given the Thornton ( 2013 ) estimate is now thought likely to be too high. In general, we expect the true rate of FRBs to be lower than what is reported due to non-publication bias. If archival data are searched and nothing is found, it is less likely to be published
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