Statistics and Probability Primer for Computational Biologists

ii Introduction Introduction Why do you need to know the theory behind statistics and probability to be proficient in computational biology? While it is true that software to analyze biological data often comes prepackaged and in a working form (sometimes), it is important to know how these tools work if we are able to interpret the meaning of their results properly. Even more important, often the software does not currently exist to do what we want, so we are forced to write algorithms ourselves. For this latter case especially, we need to be intimately familiar not only with the language of statistics and probability, but also with examples of how these approaches can be used. In this primer, our goal is to convey the essential information about statistics and probability that is required to understand algorithms in modern computational biology. We start with an introduction to basic statistical terms such as mean and standard deviation. Next we turn our attention to probability and describe ways that probabilities can be manipulated and interconverted. Following this, we introduce the concept of a discrete distribution, and show how to derive useful information from this type of model. As an extension of discrete distributions we then introduce continuous distributions and show how they can be used. Finally, we then discuss a few of the more advanced tools of statistics, such as p-values and confidence intervals. Appendix A and B cover optional material that related to more complex probability distributions and a discussion of Bayesian networks. If you are already comfortable with basic statistical terms, such as mean and variance, then feel free to skip the first chapter. In each section, our goal is to provide both intuitive and formal descriptions of each approach. To aid in providing a more intuitive understanding of the material, we have included a number of worked out examples that relate to biologically relevant questions. In addition, we also include example problems at the end of the chapter as an exercise for the reader. Answers to these problems are listed in Appendix C. Working the problems at the end of each chapter is essential to ensure comprehension of the material covered. More difficult optional problems that may require significant mathematical expertise are marked with a star next to their number.