Details of today's prediction

The prediction for each day is based on a year of data prior to the day. The following figures illustrate the process of inference for today's prediction.

Figure 1 shows the year of data as a plot of event peak flux versus time (top panel). The rate of flaring is modelled as a piecewise constant Poisson process, and the Bayesian blocks procedure (Scargle 1998, ApJ 504, 405-418) is applied to the data to determine the piecewise intervals, i.e. periods of time during which the rate is approximately constant. The resulting sequence of intervals and rates is shown in the bottom panel of Figure 1. The last Bayesian block describes the current rate, and the previous blocks give information about how the rate might be expected to vary.

Figure 1: Top panel: Year of flaring used in prediction. Bottom: Bayesian blocks decomposition of that data.

Figure 2 shows the distribution of the peak flux of the year of events as a differential distribution (top panel) and as a cumulative distribution (bottom panel), in a log-log representation. The straight line appearance of the data reflects the fact that flares obey a power-law size distribution. A power-law model (with a slope determined by the maximum likelihood method) is shown in each panel by a thick line.

Figure 2: Top panel: Differential distribution of year of events in peak flux. Bottom: Cumulative distribution in peak flux.

Based on the information on the current and prior rate obtained by the Bayesian blocks procedure and the power-law model for the size distribution, posterior distributions are constructed for epsilon, the probability of at least one flare above a specified size within one day. The sizes considered correspond to M and X class events. The resulting distributions are shown in Figure 3.

Figure 3: Top panel: Posterior distribution for M-X events. Bottom: Posterior distribution for X events.

It should be noted that these predictions are made using only past event statistics. As such they may be considered as a kind of minimal, or "baseline" prediction. A variety of observations are available of physical parameters known to associated with flaring, and in principle these additional observations could be used to improve upon the event statistics prediction.