# High level interpretation of Cramer-Rao bound and Fisher information matrix

I am reviewing a manuscript and am struggling to understand why some statistical techniques were chosen, i.e. what information they can give. The paper looks at the effect of predicting a variable such as temperature based on noisy measurements from different sensors. Can you please correct any errors in the following interpretation of the paper's statistical tools:

1. For the temperature prediction, the authors obtain a Cramer Rao Bound (CRB) which defines the smallest error that the prediction might have. A small CRB is desirable, since it means the prediction has a smaller error.
2. The authors decompose the CRB into a numerator and a divisor. The divisor is the Fisher Information Matrix (FIM). A large FIM is desirable, since it means the prediction has a smaller error.
3. The authors lists several situations that would result in a singular FIM, which is undesirable because it means that the temperature prediction isn't valid.