## Dimension effects

To see the effect of dimension on the accuracy of as predictor of the asymptotic mean of MCMC-UMS, we repeated the experiment of Figure 5.12 for various manifold dimensions . In Figure 5.13, we plotted after 20,000 full iterations of MCMC-UMS (systematic approach and whitening). Plotted is the average of for three trials at each dimension. We see that even for manifold dimension 3, there is good accuracy. Note that means that the fractional error has a standard deviation of .055 or 5.5% error. At a dimension of 125, is about .00009, a fractional error standard deviation of 1%.

Baggenstoss 2017-05-19