In many inference problems resource constraints preclude the
utilization of all available measurements. Consequently, active
approaches seek to choose the subset of measurements which maximize
the expected information gain for an underlying inference
task. Determining the optimal subset of measurements in such cases is
known to have exponential complexity. Here, we discuss performance
guarantees for tractable greedy measurement selection algorithms in
sequential estimation problems. We show that optimal choices can yield
no better than twice the performance of greedy choices for
information-theoretic measures such as mutual information and Fisher
information. The bound can be shown to be sharp. We also discuss
additional on-line computable bounds, often tighter in practice, as
well.