This raises philosophical problems: suppose that random physical processes happen on length scales both smaller than and bigger than the particle horizon.
A physical process (such as an amplitude of a primordial perturbation in density) that happens on the horizon scale only gives us one observable realization.
Because it is necessarily a large fraction of the signal, workers must be very careful in interpreting the statistical significance of measurements on scales close to the particle horizon.
[3] This is important in describing the low multipoles of the cosmic microwave background and has been the source of much controversy in the cosmology community since the COBE and WMAP measurements.
Another problem of limited sample sizes in astronomy, here practical rather than essential, is in the Titius–Bode law on spacing of satellites in an orbital system.