We compute the Lyapunov exponent of the tanh map using (10) from a finite orbit with N=10,000 points, discarding the first 200 points to eliminate the transient behavior.
If it has not foamed by this point, discard it.
For each model we sampled the posterior distribution 40,000,000 times, logging every 1,000 steps for a total of 40,000 data points, the first 10,000 data points were discarded as burn-in.
A high proportion of bending fractures shows that several of the points were discarded due to production failures, and points with impact damage or hafting traces show that used points were left in the cave.
This may be slightly less than the interpolation values used with the original data analysis, which correspond to numbers of points in the outline before redundant points are discarded.
(mathcal{W}) is a set of the grid points already discarded, and (mathcal{X}) is a set of the remaining grid points at each iteration.
In [27], the authors indicate that if (lambda =lambda (bar {s})) is a turning point of order one, then the corresponding final time t f is a conjugate time, and the corresponding point (E_{x_{0},t_{f},lambda } u(x_{0},p_{0},t_{f},lambda))) is the corresponding conjugate point 4. By assuming the absence of conjugate points over Ω for all λ∈[0,1], the possibility of turning points is discarded.
Markov chains were run for 60,000 cycles, the first 5,000 points were discarded as burn-in, and every 10th tree from the remaining points was collected to compute the posterior probabilities for individual nodes.
The first 500 and 150 points were discarded as burnin for the "CAT" and "LG" runs, respectively, and the remaining points used to compute the cross-validation log-likelihood.
