| Popis: |
We are now ready to look at particular methods of estimating parameters from data. As we will see, there is a very sophisticated methodology that has developed for these problems and, in many cases, the estimation process can be automated and turned into almost a crank-turning operation. Nonetheless, it is very important to understand in detail what we are doing, and we will discuss problems that have arisen when people were not sufficiently careful. We will discuss how the error in the estimation of a parameter using a \(\chi ^2\) fit can be a normal distribution, while the \(\chi ^2\) as a whole has a \(\chi ^2\) distribution. We discuss some problems for fitting histograms and taking the theory at the center point, and an approximate correction called Shepard’s corrections for grouping. Correlation coefficients are often poorly determined in fits and we discuss a suggested modification. Finally, we discuss a method for putting together several uncorrelated probabilities. |
