Confidence intervals

The MLE is a point estimate and as such, on its own, it is almost of no practical use. It would be more appropriate to give coverage of parameter points, which is most likely to contain the true unknown parameter. A general practice is to specify the coverage of the points through an interval and then consider specific intervals that have a specified probability. A formal definition is in order.

A confidence interval for a population parameter is an interval that is predicted to contain the parameter with a certain probability.

The common choice is to obtain either 95 percent or 99 percent confidence intervals. It is common to specify the coverage of the confidence through a significance level , more about this in the next section, which is a small number closer to 0. The 95 percent and 99 percent confidence intervals then correspond to percent intervals with respective equal to 0.05 and 0.01. In general, a percent confidence interval says that if the experiment is...