  In this chapter we review some of the basic attack constructions that exploit
a stochastic description of the state variables. We pose the state estimation
problem in a Bayesian setting and cast the bad data detection procedure as a
Bayesian hypothesis testing problem. This revised detection framework provides
the benchmark for the attack detection problem that limits the achievable
attack disruption. Indeed, the trade-off between the impact of the attack, in
terms of disruption to the state estimator, and the probability of attack
detection is analytically characterized within this Bayesian attack setting. We
then generalize the attack construction by considering information-theoretic
measures that place fundamental limits to a broad class of detection,
estimation, and learning techniques. Because the attack constructions proposed
in this chapter rely on the attacker having access to the statistical structure
of the random process describing the state variables, we conclude by studying
the impact of imperfect statistics on the attack performance. Specifically, we
study the attack performance as a function of the size of the training data set
that is available to the attacker to estimate the second-order statistics of
the state variables.
