We present information-theoretic lower bounds on the estimation error for 
problems of distributed computation. These bounds hold for a network at- 
tempting to compute a real-valued function of the global information when the 
nodes can communicate through noisy transmission channels. Our bounds are 
algorithm-independent, and improve on previous results by Ayaso et al., where 
the exponential error rate was upper-bounded by the capacity-conductance of 
the network. We show that, if the transmission channels are stochastic, the 
highest achievable exponential error rate is in general strictly smaller than the 
minimum cut-set capacity of the network. This is due to atypical channel behav- 
iors, which, despite their asymptotically vanishing probability, affect the error 
exponent.