In 1921 the British Statistician Sir Ronald Fisher (in whose honor the F-distribution is named) coined the term "likelihood" as the probability of the observed data considered as a mathematical function of a parameter. Computing the value of this parameter which maximizes the function of the data is called maximum likelihood estimation (from which a wide variety of modern statistical methods have developed). He was also aware of the problem of how to determine the amount of information for estimating these population values is contained in a random sample.
"Maximum likelihood" estimation to extract "information" contained in the data are important components of a branch of statistics called Generalized Linear Models. This includes a wide variety of statistical models which can be defined by one general mathematical equation for models that belong to the exponential family. The choices are flexible enough to allow the type of data to define what particular model should be chosen for analysis (in contrast to attempting to apply one model to analyze many types of data). These include familiar techniques to analyze continuous data that follow the normal distribution to relatively unknown methods for categorical data expressed as counts that follow the binomial, Poisson, or negative binomial distributions.
The novel idea of measuring information supplied by data to estimate unknown parameters is the first use of "information" in a technical sense in statistics. The variance/covariance matrix of the parameters, so ubiquitous in statistical analysis, evolves from the idea that good information (that is, the amount and quality of data) will provide good estimates of the population parameters. In fact, this concept is why the name "Fisher Information Matrix" has been attached to it and lies at the center of statistical data analysis yet today.
Many books and journal articles have been written on this very broad topic of generalized linear models that are available within the SAS procedure called GENMOD. Many of them are also available in numerous other SAS procedures which will also be illustrated and referred to as needed. However, the focus of these links found below are of examples with data analysis through PROC GENMOD.