Part I of this book is devoted to outlining the basic principles of algebraic statistics and their relationship to computational biology. Although some of the ideas are complex, and their relationships intricate, the underlying philosophy of our approach to biological sequence analysis is summarized in the cartoon on the cover of the book. The fictional character is DiaNA, who appears throughout the book, and is the statistical surrogate for our biological intuition. In the cartoon, DiaNA is walking randomly on a graph and is tossing tetrahedral dice that can land on one of the letters A, C, G or T. A key feature of the tosses is that the outcome depends on the direction of her route. We, the observers, record the letters that appear on the successive throws, but are unable to see the path that DiaNA takes on her graph. Our goal is to guess DiaNA's path from the die roll outcomes. That is, we wish to make an inference about missing data from certain observations.

In this book, the observed data are DNA sequences. A standard problem of computational biology is to infer an optimal alignment for two given DNA sequences. We shall see that this problem is precisely our example of guessing DiaNA's path. In Chapter 4 we give an introduction to the relevant biological concepts, and we argue that our example is not just a toy problem but is fundamental for designing efficient algorithms for analyzing real biological data.