Sampling effects like this can be really pernicious for network data (and I imagine similarly for other dependent data). It can be difficult to tell if a network is scale-free from observing a subnetwork [1] or impossible to learn an ERGM (basically, a maximum entropy distribution with graph properties as its statistics) from a subnetwork [2].
Sampling effects like this can be really pernicious for network data (and I imagine similarly for other dependent data). It can be difficult to tell if a network is scale-free from observing a subnetwork [1] or impossible to learn an ERGM (basically, a maximum entropy distribution with graph properties as its statistics) from a subnetwork [2].
[1] M. P. H. Stumpf, C. Wiuf, and R. M. May, “Subnets of scale-free networks are not scale-free: sampling properties of networks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 12, p. 4221, 2005.
[2] C. Shalizi, “Consistency under Sampling of Exponential Random Graph Models,” arXiv.org. 2011.
Incidentally, Pearl’s original explanation in Chapter 1 of Causality is here; the whole first edition of the book is available online here.
That was quite good.