Details

For pedagogical purposes, this Demonstration finds maximum likelihood estimators using a general approach. In specific cases, more efficient and swifter computational methods may exist. In particular, optimal parameter values in the case of normally distributed error can be obtained via linear least-squares optimization; the maximum likelihood estimate of the standard deviation can be obtained as the square root of the mean of the squared residuals. The code underlying this Demonstration permits this swifter but less general methodology to be used.

This Demonstration will be more responsive to movements of the parameter sliders if no computation of the maximum likelihood estimate is requested.

A useful experiment is to set the parameter sliders so that they correspond to the optimal parameter values determined by the computer. Then determine the effect on the sum of the log likelihoods as the σ parameter increases. Then see what happens if you set the α and β parameter sliders to suboptimal levels. Does increasing increase or decrease the sum of the log likelihoods?