  This work considers finding optimal positions for the electrodes within the
Bayesian paradigm based on available prior information on the conductivity; the
aim is to place the electrodes so that the posterior density of the
(discretized) conductivity, i.e., the conditional density of the conductivity
given the measurements, is as localized as possible. To make such an approach
computationally feasible, the complete electrode forward model of impedance
tomography is linearized around the prior expectation of the conductivity,
allowing explicit representation for the (approximate) posterior covariance
matrix. Two approaches are considered: minimizing the trace or the determinant
of the posterior covariance. The introduced optimization algorithm is of the
steepest descent type, with the needed gradients computed based on appropriate
Fr\'echet derivatives of the complete electrode model. The functionality of the
methodology is demonstrated via two-dimensional numerical experiments.
