Burn-in M number of deleted values is small, meaning that starting values are not very influent.
Total N is the advised number of iterations, which is actually quite close to our "choice" (=2000)
Lower bound Nmin is the minimum sample size based on zero autocorrelation. Here it is relatively low, so it is a good point.
Dependence factor I informs about the dependence into the chains, or the extent to which autocorrelation inflates the required sample size. It is common to say that values above 5for this criterion indicate a strong autocorrelation. Here we see that it is slightly the case, especially for $\xi$.