INTERVAL ESTIMATION USING THE LIKELIHOOD FUNCTION

The general properties of two commonly-used methods of interval estima tion for population parameters in physics are examined. Both of these methods employ the likelihood function: (i) Obtaining an interval by f inding the points where the likelihood decreases from its maximum by s ome specified ratio; (ii) Obtaining an interval by finding points corr esponding to some specified fraction of the total integral of the like lihood function. In particular, the conditions for which these methods give a confidence interval are illuminated, following an elaboration on the definition of a confidence interval. The first method, in its g eneral form, gives a confidence interval when the parameter is a funct ion of a location parameter. The second method gives a confidence inte rval when the parameter is a location parameter. A potential pitfall o f performing a likelihood analysis without understanding the underlyin g probability distribution is discussed using an example with a normal likelihood function.