A User Manual for the Fisher Information Matrix

The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signal-to-noise ratios, or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. I discuss these pitfalls and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi-)singular Fisher matrices, and how do we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signal-to-noise ratio high enough to believe the Fisher-matrix result?