(This GitHub repository contains files and information for my book Bayesian A/B Decision Models)
Bayesian A/B decision models have evolved significantly in statistical analysis and decision-making, especially over the last decade. This preface introduces my book, "Bayesian A/B Decision Models," which encapsulates my experience utilizing these models in highly specialized areas such as auditing and as an expert witness in computing damages for corporate and industrial business legal cases.
My journey began with a recognition that, while traditional statistical methods provided valuable insights, they often fell short in addressing complex, real-world problems where nuanced decision-making is crucial. The Bayesian A/B decision approach, although initially daunting due to its complexity and the steep learning curve, offered a robust alternative. The startup costs -- both in time and effort -- to master this advanced statistical tool are nontrivial, yet the benefits it brought to my professional capabilities were well worth the effort.
As a consultant and legal expert, the flexibility of Bayesian A/B models proved invaluable. These models allowed me to respond adeptly to diverse and dynamic requests for detailed analytical reports. I found myself capable of producing specific financial analyses and outcomes that were not only highly tailored but also often unattainable by the opposing side using more traditional methods. This edge was instrumental in numerous legal and corporate deliberations, where precision and adaptability of the statistical analysis could make or break a case.
Over the years, my engagement with Bayesian A/B models has evolved, revealing applications that spanned various sectors and challenges. This book is not merely a reflection of my own experiences but also serves as a guide to applying Bayesian decision models across nearly every imaginable scenario. The examples included range from healthcare, marketing, and finance to more niche sectors where traditional A/B testing or frequentist approaches might falter due to their inherent limitations.
One of the unique aspects of Bayesian A/B testing is its requirement for a powerful, flexible statistical language that can handle the complexity and nuances of Bayesian analytics. Throughout my practice, I have found the R statistical language to be a singularly effective and efficient tool for the implementation of my ideas and models. It not only supports the necessary statistical rigor but also provides a versatile platform for developing, testing, and deploying Bayesian models.
To this end, I have included a comprehensive technical appendix in this book, which contains a complete set of R code for all the examples discussed. This resource aims to not just illustrate the theoretical application of Bayesian A/B tests but to also provide practical tools that can be adapted and implemented by readers in their own fields. For those who prefer a digital format or wish to interact with the code directly, all resources are available on my GitHub site at https://github.com/westland/BayesAB. Whether you are a seasoned statistician, a budding analyst, or a professional curious about the potential of Bayesian A/B testing, this book offers a comprehensive overview and detailed applications that demonstrate the unparalleled benefits of this approach.
I sincerely hope that this book not only enlightens you about the sophisticated world of Bayesian A/B testing but also encourages you to explore its potential in your own areas of expertise. The journey from a novice to a proficient user of Bayesian models is challenging yet rewarding, and it is a path I recommend enthusiastically to all who are committed to excellence in decision-making and statistical analysis. Over a century ago, scholars like Ronald Fisher, Karl Pearson, J.B.S. Haldane, and William Sealy Gosset devised the frequentist statistical decision framework used up to the current day. Working with nothing more than pen, paper, and rudimentary adding machines, these pioneers crafted their mathematics to be as simple as possible, often at the expense of accuracy. They tackled the complexities of their era with squared-error loss functions and optimization through differential calculus, a testament to their ingenuity and dedication.
In their time, these brilliant minds were not just solving statistical problems; they were framing a new perspective on the world, one calculation at a time. Their objectives might have been different, reflecting the unique challenges and limited technological resources of their age, but their legacy is undeniable.
Fast forward to today, and the landscape of statistical modeling has transformed dramatically. Armed with virtually unlimited computational power and expansive memory capacities, we stand on the shoulders of these giants, exploring a vast array of possibilities that extend far beyond their imaginations and methods. Yet too often, out of habit or tradition, we cling to antiquated and inefficient methods.
In particular, the cornerstone of modern statistical A/B decisions is the Neyman-Pearson Lemma, foundational to the frequentist approach that dominates contemporary A/B testing scenarios. Statistician Bruce Hill, who was one of my PhD mentors, would illustrate the inherent limitations of such frequentist approaches with examples like the Behrens-Fisher problem, which is deemed insurmountable from a frequentist perspective, but is not a problem at all when viewed through a Bayesian lens. Bayesians embraces a powerful, flexible approach to statistics that asks "How much have we learned?" rather than "What is the absolute truth?" Absolute truths are elusive, and prejudiced by the questions we ask, the things we measure, and the limitations of our finite minds. But Bayesians know that there is always the opportunity to learn. Bayesians view every new piece of data as part of a never-ending puzzle, a chance to learn and refine our understanding incrementally.
Our exploration into bandit problems revealed that while traditional frequentist methods might reach approximate solutions if one has sufficient computational firepower, Bayesian methods offer an intuitive, straightforward way to make decisions. Bayesians appreciate the inherent uncertainties of the world, recognizing that not everything can be known. Yet, with controlled data collection at manageable costs, Bayesians continually enhance their understanding, tuning the pace and quality of their learning to meet practical needs.
Our journey into the science of informed decision-making has been as much about the methods we use to summarize and interpret data as it has been about the philosophical underpinnings that guide these choices. Bayesian innovations in A/B decision models not only allow us to utilize all available data but also enable us to learn efficiently from this data and make the best possible choices