Estimation Problems
Lawrence N. Dworsky · 2019
An important use of Bayes Theorem is for estimating parameters in a situation where there is limited information. The locomotive problem is an example of this estimation category of calculations. To improve the estimate of the number of locomotives, people need more information. This can be in either or both of two categories: learn more about the statistics of the locomotive business so that people can improve their prior distribution, and spot some more locomotives so that they have more data. The lighthouse problem and its mathematical equivalent are “standard” examples of parameter estimation using Bayes Theorem. The likelihood function is the probability of a detector at xk capturing a flash of light if the light is at xp. As the number of data points continues to increase, the curve “settles in” to peaking at the actual location point of the lighthouse and the confidence interval narrowing as the number of data points increases.