Maximum Likelihood and Other Methods to Estimate Variables

Abstract

In this chapter we study the problem of estimating parameters of the distribution function of a random variable when N observations of the variable are available. We discuss methods that establish what sample quantities must be calculated to estimate the corresponding parent quantities. This establishes a firm theoretical framework that justifies the definition of the sample variance as an unbiased estimator of the parent variance, and the sample mean as an estimator of the parent mean. One of these methods, the maximum likelihood method, will later be used in more complex applications that involve the fit of two-dimensional data and the estimation of fit parameters. The concepts introduced in this chapter constitute the core of the statistical techniques for the analysis of scientific data.