14.1 Bayesian Statistics
There has been an extensive development of the ideas presented in this book within the field of statistics. Statistics (in the singular) is the art and science of studying statistics (in the plural), namely data, typically in numeric form, on a variety of topics. An early historical example was the collection of data on the production of wheat every year. Nowadays statistics covers any topic in which data are available, in particular within the scientific method. Once the data are available, statisticians have the task of presenting and analyzing them and, as a result, the activity of statistics (in the singular) has been developed. Within science, most of the effort has been devoted to models where, as we have seen, data, now denoted by x, are modeled in terms of a parameter , through a probability distribution of x for each value of , . A simple example is the measurement x of the strength of a drug, where there will be uncertainty because all people do not react in the same way to the drug. If x contains measurements on several people, ...