Relative estimation errors of three different decoders, computed on responses of an optimized heterogeneous population. All results are presented relative to the true Bayes least squares (BLS) decoder (e.g., a value of 1 indicates performance equal to the BLS). a The Bayesian population vector accurately approximates the true BLS estimator (in terms of mean squared error) over a wide range of resource constraints, and converges as the number of neurons increases. b The standard population vector has substantially larger error (note scale), and fails to converge to BLS performance levels. c Optimizing the weights of a population vector leads to a significant performance increase, but the resulting estimator is still substantially worse than the BPV and again fails to converge.