“…The posterior probability density functions for the physical parameters, i.e., E k,iso,on , Γ 0 , θ c , θ jet /θ c , θ v /θ c , p, ǫ e , ǫ B , A * , and R tr , are presented in Figure 8, where only the fitting result of GRB 120326A is shown as an example. The optimal result from MCMC fitting is shown in Figure 7 with blue line (XRT) and red line (optical), and the obtained parameters at the 1σ confidence level are reported in Table 1, where the values of the transition radius R tr (i.e., 1.05 × 10 17 cm, 6.31 × 10 16 cm, and 3.98 × 10 17 cm for GRBs 120326A, 120404A and 100814A, respectively) are consistent with those found in other bursts (e.g., Kong et al 2010;Feng & Dai 2011a;Ramirez-Ruiz et al 2001;Li et al 2020). It can be found that both the X-ray afterglow and the optical afterglow of these bumps can be well modelled with an off-axis observed external-forward shock in a free-to-shocked wind environment.…”