An Interest in Statistics:
George Box, a British-born scientist, developed an interest in statistics while working as a chemist on laboratory experiments.

Formal Education:
Box pursued his formal education in statistics, culminating in a PhD from the University of London in 1952.

Career Highlights:
He led the statistics group at the Dyestuffs Division of Imperial Chemicals Industries in England in the mid-1950s. In 1957, Box moved to the United States to direct the Statistical Techniques Research Group at Princeton University. In 1960, he joined the University of Wisconsin and founded the statistics department there.

Contributions to Statistics:
Box made significant advancements in response surface methodology and evolutionary operation. He also contributed to time series analysis, robustness, inference, and other areas. His work was driven by practical problems, leading to impactful solutions.

Publications and Recognition:
Box authored over 110 research papers and co-authored six books. He received major awards from renowned organizations, including the Royal Statistical Society and the American Statistical Association.

Fellowships and Memberships:
Box was a fellow of prestigious organizations such as the American Academy of Arts and Sciences and the American Statistical Association.

Getting Started in Statistics:
George Box’s initial background was in chemistry. His involvement in chemical warfare research during World War II led to his interest in statistics. He recognized the need for statistical analysis to interpret experimental data and improve chemical processes.

Inspiration from Fisher’s Statistical Methods Research Workers:
Box had limited prior knowledge of statistics, but he found a book by R.A. Fisher called “Statistical Methods for Research Workers” and attempted to understand it. He was tasked with designing and analyzing experiments in the absence of a statistician.

Learning through Self-Study and Collaborations:
Box continued to work in experimental design and analysis for over three years during the war. He requested reading materials from the army educational department, leading to a list of mostly Fisherian books. These books provided a strong foundation in experimental design, sampling methods, and applications in various fields.

Seeking Expert Guidance:
Box encountered challenges and sought guidance from Professor Cameron, a pathologist with an interest in mathematics. Cameron suggested consulting R.A. Fisher, recognizing his approachability. Box wrote to Fisher, who invited him to Cambridge to discuss his data.

Transforming Data with Fisher’s Guidance:
Fisher suggested a reciprocal transformation to linearize the time mortality data that Box was struggling with. Box made the transformation and found that the data became parallel and approximately straight lines. Fisher directed Box to an appendix in a paper by Bliss to address the censored data issue.

Addressing Theoretical Understanding:
Box expressed concerns about his lack of statistical theory knowledge. Fisher provided Box with Volume One of M.G. Kendall’s book on statistical theory as a resource for further learning.

Collaboration and Mentorship:
Box’s interaction with Fisher highlights the importance of seeking expert guidance and mentorship in advancing statistical knowledge and skills. Their collaboration exemplifies the power of collaboration between statisticians and practitioners in solving real-world problems.

Educational Journey:
After serving in the military, George Box pursued a career in statistics. He enrolled at University College in 1945, seeking admission to study statistics.

Admission to University College:
Box had an informal interview with Egan Pearson, during which he expressed his admiration for R.A. Fisher’s work. Pearson granted Box admission, noting that other statisticians besides Fisher had made significant contributions.

Summer Jobs and Practical Experience:
Box sought summer jobs to gain practical experience in statistics. During his first summer, he worked at Imperial Chemical Industries (ICI) headquarters in London, assisting with the revision of a book on statistical methods.

Vacation Job at ICI’s Dyestuff’s Division:
Box spent his second summer vacation at ICI’s Dyestuff’s division in Blakely, Manchester. He worked in a testing lab, conducting various experiments on materials like vinyl plastics and rubber.

Applying Statistical Methods in Testing:
Box utilized his knowledge of statistical designs, such as factorials, Latin squares, and incomplete block designs, to analyze the experimental data. He efficiently designed experiments with limited resources, considering factors and running tests in small blocks.

Partial Confounding and Research Focus:
Box explored partial confounding techniques to optimize the efficiency of experiments with multiple factors. His research focused on developing statistical methods for industrial applications, particularly in the chemical industry.

Influences at University College:
George Box was concerned about the appropriateness of testing procedures at ICI that assumed normality when the actual distribution was non-normal. He questioned the use of analysis of variance on correlated repeated measures data.

Research at ICI:
Box investigated the use of fractional factorial designs to optimize experimental conditions for chemical processes. He collaborated with chemists to improve the yield of a chemical process through experimental design.

Collaboration with Wilson and Chemists:
Box worked closely with chemist K.B. Wilson and other chemists to develop methods for optimizing experimental conditions. This collaboration led to the publication of a paper with Wilson on the use of steepest descent methods for process optimization.

Challenges in Full-Scale Implementation:
Box and colleagues faced difficulties in getting manufacturers to agree to run experiments on full-scale processes. When they were able to conduct a 2^3 factorial design with a center point on a full-scale process, the first-order effects were small, and the second-order interactions were large and significant.

Development of Composite Design:
Box proposed determining all the second derivatives, including curvature derivatives, to better understand the process. Jules, a colleague, was hesitant to run a 3-level design due to the large number of runs required. Box suggested using a composite design with two additional points at each level of the cube, resulting in a total of 15 runs.

Publication and Recognition:
The paper on composite design was published with Wilson and received positive feedback from the Royal Statistical Society. The work gained recognition, leading to an invitation to present the paper at the Royal Statistical Society.

Move to the United States:
Box’s involvement in the composite design paper played a role in his move to the United States. Stu Hunter, a student at Raleigh who knew Gertrude Cox, recommended Box for a position at the University of North Carolina at Chapel Hill.

Arrival in the United States:
George Box received an unexpected invitation to visit North Carolina State College as a visiting research professor through the efforts of Frank Grubbs and Bob Hader. ICI granted him a year’s leave of absence and paid for his travel expenses.

Research at North Carolina State College:
Box collaborated with Stu Hunter on response services, particularly rotatable designs. He also worked with Sig Anderson on robustness and its relation to randomization tests.

Origin of Evolutionary Operation (EVOP):
During a boat trip to the Thousand Islands, Box conceived the idea of EVOP while discussing designs with Sig Anderson. The concept involved running a full-scale process in the center and then moving out to slightly modified processes along various rays, returning to the center periodically.

Work on EVOP and Nonlinear Estimation upon Return to England:
Box continued his research on EVOP upon returning to ICI. He collaborated with Philip Yule, a physical chemist, to link the observed process maxima to chemical kinetics. This led them to develop methods for nonlinear estimation, initially using response surface techniques and later adopting the Gauss method of linearization.

Return to the United States:
The circumstances that brought Box back to the United States are not mentioned in the given text.

Research Topics:
George Box continued his research in robustness, specifically in robustness in regression analysis and randomization. He also worked on standard designs, fractionals, responsive designs, and non-linear designs, collaborating with Stu Hunter and Curley Lucas.

Time Series Analysis:
Box’s involvement in time series analysis originated from a problem he encountered in experimental design. He sought to develop a method to chase the optimum conditions in a process that changed over time, such as in a chemical process. This led him to consider the dynamics of the system and the correlation of noise, eventually recognizing it as a control problem.

Collaboration with Gwilym Jenkins:
Box’s discussions with Gwilym Jenkins about the dynamics of systems and correlated noise led them to realize that the problem they were addressing was a control problem, which in turn was related to time series problems. This collaboration sparked their interest in time series analysis and laid the foundation for their groundbreaking work in the field.

Statistical Collaboration with Olaf Haugen:
Box and Haugen collaborated on studying a gas furnace reaction involving the burning of methane to produce CO2. The goal was to investigate time series analysis and control theory in a practical industrial context. The project led to the development of equipment and the generation of data that were later featured in the Waxman-Jenkins book.

Interest in Bayesian Theorem:
Box’s early education in statistics emphasized frequentist theory, with warnings against Bayesian approaches. As he began teaching advanced series statistics at the University of Wisconsin, he found himself increasingly drawn to Bayesian concepts. The practical challenges of working with insufficient statistics and other limitations of frequentist methods led him to see the advantages of Bayesian theorem.

Influence on George Tao:
Another student in Box’s advanced series statistics class was George Tao, who went on to become a prominent statistician. Box’s teaching and guidance had a significant impact on Tao’s intellectual development and career trajectory. Tao’s subsequent work and contributions to statistics reflect the influence of Box’s teachings and the Bayesian perspective.

Motivations for Collaboration:
Collaboration between George Box and others was driven by practical problems, such as the robustness of Bayes’ theorem, time series analysis, and environmental data analysis.

Intervention Analysis:
Environmental data analysis led to the development of intervention analysis to assess the impact of changes in regulations, such as Rule 63 in Los Angeles County, on environmental variables.

Theory of Modeling:
The theory of modeling emerged from various ingredients, including work on modeling aspects, discrimination between models, and time series analysis.

Criticism and Estimation in Modeling:
Box identified a twofold iteration in model building involving criticism and estimation. Models are initially assumed to be correct, and parameters are estimated using Bayes or likelihood methods. Models are then criticized by examining residuals and other diagnostics. This iterative process continues until the model converges and becomes more certain.

Practical Problems Leading to Theoretical Advances:
Box emphasizes the importance of working on practical problems and using those experiences to drive theoretical advances.

Transformations:
The collaboration between Box and David Cox on transformations was an exception to the pattern of practical problems leading to theoretical advances. The precipitating event for their work on transformations was a suggestion from colleagues that they should write a paper together. They eventually overcame a sticking point and completed the work, although it was not directly motivated by a specific practical problem.

Conclusion:
Box reflects on his career as a statistician, highlighting the importance of practical problems in driving theoretical advances and the value of transformations in modeling.

Opportunities for Collaboration and Learning:
George Box highlights the advantages of being a statistician, emphasizing the opportunities for collaboration and learning across various disciplines. He mentions that statisticians have the chance to engage with a diverse range of fields, including geology, astronomy, and chemistry, leading to a broader perspective and deeper understanding of science.

Horizontal vs. Vertical Organization:
Box contrasts the horizontal nature of statistics with the more vertical structure of other fields, such as chemistry. In statistics, one can explore different areas and interact with a wider range of experts, gaining a comprehensive view of various scientific domains.

Exposure to Diverse Problems and People:
Box emphasizes the exposure to diverse problems and people as a key benefit of being a statistician. He shares an anecdote from his time at ICI, where his involvement in multiple departments provided him with a unique perspective and insights into the company’s operations.

Encouragement for Beginners:
Box encourages individuals starting in statistics to explore the exciting problems waiting to be solved in various fields. He mentions specific organizations, such as Bell Labs, Boyce-Thompson Institutes, and cotton research institutes, as potential places where statisticians can make significant contributions.

Theoretical Developments from Practical Work:
Box believes that engaging with practical problems in different fields can lead to the discovery of new theoretical concepts and advancements. He suggests that statisticians can contribute to the development of new theoretical frameworks by addressing real-world challenges.