Since the weak∗ convergence implies the coordinatewise convergence, standard arguments show that limsup_{n} I_{Phi}(x_{n}+x)=limsup _{n} I_{Phi}(x_{n})+I_{Phi}(x) for every (xinell_{Phi}) and for every (w^ -null sequence ({x_{n}} ).
In all Bayesian analyses, comparison of parallel runs showed posterior probability convergence (standard deviation <0.01) and likelihood equilibrium, were reached within the burn-in phase.
At convergence, standard deviations, and 68% and 95% confidence intervals for all fluxes were calculated using the parameter continuation technique [ 41].
In the MrBayes analyses, we used two simultaneous runs of Markov chain Monte Carlo sampling, and the runs were terminated upon convergence (standard deviation of the split frequencies <0.01).
Two independent runs with four Markov Chain Monte Carlo chains were run for 10 million generations and sampled every 1000 generations to achieve convergence (standard deviation of split frequencies < 0.02).
Consequently, we classify a variant that exhibits extremely slow EM convergence, as evidenced by failure to achieve a standard convergence criterion of 10−8 in 100 iterations, as uninformative with respect to the model and thus likely to produce poor estimates of the posterior genotype distribution.
The marching window satisfies the same convergence criterion as the standard pseudo-time-stepping methods, hence resulting in the same converged solution within the tolerance of the user-specified convergence threshold.
Finally, it is important to note that, the speedups reported here are smaller than those reported previously (Stamatakis and Ott, 2008b) because of a bug in the branch length optimization convergence criterion under the standard model, that has been fixed in the latest release (v 7.2.6) of RAxML.
Gray thinks the pursuit of convergence on standards is a delusion, kept alive in the face of repeated failure by cognitive dissonance.
