  One can often make inferences about a growing network from its current state
alone. For example, it is generally possible to determine how a network changed
over time or pick among plausible mechanisms explaining its growth. In
practice, however, the extent to which such problems can be solved is limited
by existing techniques, which are often inexact, inefficient, or both. In this
article we derive exact and efficient inference methods for growing trees and
demonstrate them in a series of applications: network interpolation, history
reconstruction, model fitting, and model selection.
