"Information" is defined mathematically in information theory. Many books including this theory are for communication engineering.
The quantity "information" is used in Statistics . I am interested in information theory related with statistics.
This method is used to evaluate the validity of statistical model.
Information criterion is the index to compare different models. There are AIC (Akaike's Information Criterion), BIC and GIC.
Information defined by Shannon used same mathematics with statistical mechanics. So results of statistical mechanics are used in information theory. Theories of heat and information have same structure.
In information theory, there is Fisher information matrix. The name "Fisher" is seen in Distribution (F-distribution), ANOVA and Design of Experiments , and those names are for same person. When I make this site, I know my works depend on him.
I studied more about information theory. The page " Artificial Intelligence " is one of them.