Parameter estimation I
Devinderjit Singh Sivia · 2006
Abstract Parameter estimation is a common data analysis problem. Like Laplace, for example, we may be interested in knowing the mass of Saturn; or, like Millikan, the charge of the electron. In the simplest case, we are only concerned with the value of a single parameter; such elementary examples are the focus of this chapter. They serve as a good introduction to the use of Bayes ‘ theorem, and allow for a discussion of error-bars and confidence intervals. Let us begin with the analysis of data from a simple coin-tossing experiment. Suppose I told you that I had been to Las Vegas for my holidays, and had come across a very strange coin in one of the casinos; given that I had observed 4 heads in 11 flips, do you think it was a fair coin? By fair, we mean that we would be prepared to lay an even 50 : 50 bet on the outcome of a flip being a head or a tail. In ascribing the property of fairness (solely) to the coin we are, of course, assuming that the coin-tosser was not skilled enough to be able to control the initial conditions of the flip (such as the angular and linear velocities).