  Information and individual activities often spread globally through the
network of social ties. While social contagion phenomena have been extensively
studied within the framework of threshold models, it is common to make an
assumption that may be violated in reality: each individual is able to observe
the neighbors' states without error. Here, we analyze the dynamics of global
cascades under uncertainty in an otherwise standard threshold model. Each
individual uses statistical inference to estimate the probability distribution
of the number of active neighbors when deciding whether to be active, which
gives a probabilistic threshold rule. Unlike the deterministic threshold model,
the spreading process is generally non-monotonic as the inferred distribution
of neighbors' states may be updated as a new signal arrives. We find that
social contagion may arise as a self-fulfilling event in that misperception may
trigger a cascade in regions where cascades would never occur under certainty.
