Statistical Rethinking

4 Linear Models

History has been unkind to Ptolemy. Claudius Ptolemy (born 90 CE, died 168 CE) was an Egyptian mathematician and astronomer, most famous for his geocentric model of the solar system. These days, when scientists wish to mock someone, they might compare him to a supporter of the geocentric model. But Ptolemy was a genius. His mathematical model of the motions of the planets (FIGURE 4.1) was extremely accurate. To achieve its accuracy, it employed a device known as an epicycle, a circle on a circle. It is even possible to have epi- epicycles, circles on circles on circles. With enough epicycles in the right places, Ptolemy's model could predict with accuracy greater than anyone had achieved before him. And so the model was utilized ...