It is not possible to re-position them, so use text objects to create the axis labels in the appropriate positions.
Try something like this example:
figure
scatter(randn(1,50), randn(1,50))
set(gca, 'XAxisLocation','origin', 'YAxisLocation','origin')
xl = xlim;
yl = ylim;
text(min(xl), 0, 'Prediction of proposed probabalistic model', 'Rotation',90, 'VerticalAlignment','bottom', 'HorizontalAlignment','center')
text(0, min(yl), 'Experimental data', 'VerticalAlignment','top', 'HorizontalAlignment','center')
It will likely be necessary to change only the string objects (desired axis labels) in this code.
It may be necessary to make a few other adjustments to get the desired appearance.
.
