Article

Modeling with Data: Tools and Techniques for Scientific Computing

Ben Klemens

PREFACE

Should you use the book? This book is intended to be a complement to the standard stats textbook, in three ways.

First, descriptive and inferential statistics are kept separate beginning with the first sentence of the first chapter. I believe that the fusing of the two is the number one cause of confusion among statistics students.

Once descriptive modeling is given its own space, and models do not necessarily have to be just preparation for a test, the options blossom. There are myriad ways to convert a subjective understanding of the world into a mathematical model, including simulations, models like the Bernoulli/Poisson distributions from traditional probability theory, ordinary least squares, and who knows what else.

If those options aren’t enough, simple models can be combined to form multilevel models to describe situations of arbitrary complexity. That is, the basic linear model or the Bernoulli/Poisson models may seem too simple for many situations, but they are building blocks that let us produce more descriptive models. The overall approach concludes with multilevel models as in, e.g., Eliason (1993), Pawitan (2001) or Gelman & Hill (2007).

Second, many stats texts aim to be as complete as possible, because completeness and a thick spine give the impression of value-for-money: you get a textbook and a reference book, so everything you need is guaranteed to be in there somewhere.

But it’s hard to learn from a reference book. So I have made a solid effort to provide a narrative to the important points about statistics, even though that directly implies that this book is incomplete relative to the more encyclopedic texts. For example, moment generating functions are an interesting narrative on their own, but they are tangential to the story here, so I do not mention them.

Computation
The third manner in which this book complements the traditional stats textbook is that it acknowledges that if you are working with data full time, then you are working on a computer full time. The better you understand computing, the more you will be able to do with your data, and the faster you will be able to do it.

People like to characterize computing as fast-paced and ever-changing, but much of that is just churn on the syntactic surface. The fundamental concepts, conceived by mathematicians with an eye toward the simplicity and elegance of pencil-and paper math, have been around for as long as anybody can remember. Time spent learning those fundamentals will pay off no matter what exciting new language everybody happens to be using this month.

I spent much of my life ignoring the fundamentals of computing and just hacking together projects using the package or language of the month: C++, Mathematica, Octave, Perl, Python, Java, Scheme, SPLUS, Stata, R, and probably a few others that I’ve forgotten. Albee (1960, p 30) explains that “sometimes it’s necessary to go a long distance out of the way in order to come back a short distance correctly;” this is the distance I’ve gone to arrive at writing a book on data-oriented computing using a general and basic computing language. For the purpose of modeling with data, I have found C to be an easier and more pleasant language than the purpose-built alternatives—especially after I worked out that I could ignore much of the advice from books written in the 1980s and apply the techniques I learned from the scripting languages.

WHAT IS THE LEVEL OF THIS BOOK? The short answer is that this is intended for the graduate student or independent researcher, either as a supplement to a standard first-year stats text or for later study. Here are a few more ways to answer that question:

Ease of use versus ease of initial use: The majority of statistics students are just trying to slog through their department’s stats requirement so they can never look at another data set again. If that is you, then your sole concern is ease of initial use, and you want a stats package and a textbook that focus less on full proficiency and more on immediate intuition.1[1]

Conversely, this book is not really about solving today’s problem as quickly as physically possible, but about getting a better understanding of data handling, computing, and statistics. Ease of long-term use will follow therefrom.

Level of computing abstraction: This book takes the fundamentals of computing seriously, but it is not about reinventing the wheels of statistical computing. For example, Numerical Recipes in C (Press et al., 1988) is a classic text describing the algorithms for seeking optima, efficiently calculating determinants, and making random draws from a Normal distribution. Being such a classic, there are many packages that implement algorithms on its level, and this book will build upon those packages rather than replicate their effort.

Computing experience: You may have never taken a computer science course, but do have some experience in both the basics of dealing with a computer and in writing scripts in either a stats package or a scripting language like Perl or Python.

Author

Computational detail: This book includes about 80 working sample programs.

Code clarifies everything: English text may have a few ambiguities, but all the details have to be in place for a program to execute correctly. Also, code rewards the curious, because readers can explore the data, find out to what changes a procedure is robust, and otherwise productively break the code.

That means that this book is not computing-system-agnostic. So if you are a devotee of a stats package not used here, then why look at this book? Although I do not shy away from C-specific details of syntax, most of the book focuses on the conceptual issues common to all computing environments. If you never look at C code again after you finish this book, you will still have a better grounding for effectively working in your preferred programming language.

Linear algebra: You are reasonably familiar with linear algebra, such that an expression like X−1 is not foreign to you. There are a countably infinite number of linear algebra tutorials in books, stats text appendices, and online, so this book does not include yet another.

Statistical topics: The book’s statistical topics are not particularly advanced or trendy: OLS, maximum likelihood, or bootstrapping are all staples of first-year grad-level stats. But by creatively combining building blocks such as these, you will be able to model data and situations of arbitrary complexity.

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[1] I myself learned a few things from the excellently written narrative in Gonick & Smith (1994).