Chapter 3. The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions

Questions on numerical precision and rounding errors with a wide range of applications are especially considered within the area of numerical mathematics. But statistics and data science are also tangled with problems on rounding and numerical precision, and data scientists should be aware of this. Of course, such problems also depend on the architecture of the computer. Even numbers that are measured with the highest degree of precision cannot be represented exactly on a computer. Some of the problems are of a general nature. It becomes critical if, for example, analytical properties of estimators differ in theory (on paper) and practice (with computers).

The goal of this chapter is to raise awareness of the mentioned topics. The reader should be sensitized to the concepts of machine numbers and rounding, as well as issues in convergence and the condition of problems. These concepts...