Noel: Chris was my PhD student at Iowa State University in the early to mid 1990s. He was a co-major in Statistics and Atmospheric Science and brought an interest in spatio-temporal processes from the perspective of atmospheric-science dynamics to our interactions. When Chris graduated in 1996 he had already accepted a postdoctoral position at the National Center for Atmospheric Research in Boulder, CO in the Geophysical Statistics Project. It was there that, along with Mark Berliner, we were able to bring the development of the hierarchical approach to spatio-temporal statistical modelling.

2. What were your main objectives during the writing process? What did you set out to achieve in reaching your readers?

Spatio-temporal statistics is rapidly evolving. Our goal was to lay out a foundation for spatio-temporal modelling that was based in hierarchical (conditional probability) thinking. We wanted to build these principles from ground zero, and to illustrate them with examples in purely spatial, temporal, and ultimately, spatio-temporal models.

3. Were there areas that you found more challenging to write and if so, why?

The areas that are least developed in the literature, such as multivariate spatio-temporal models, and spatio-temporal point processes were more difficult to write simply because there is less of a sense of what the standard approaches should be at this point.

4. Reviews are very enthusiastic about the book, one on Amazon already looking forward to a second edition with even further information! One published in Springer’s Mathematical Geosciences says ‘It is a book written by statisticians, but modern scientists trained to handle spatio-temporal data should not find the notation and language barrier insurmountable’ and ‘careful reading will surely have a large payoff’. Did you see that there was a gap in the market for this book for spatial statistics courses?

Although we felt like there were several good choices for spatial statistics courses, depending on level, we felt like there were no ideal books for a course on spatio-temporal statistics. It is interesting that spatio-temporal statistics has traditionally been considered a component of spatial statistics. By taking on this project, we wanted to show that spatio-temporal statistics has grown to the point where it is really its own discipline. In fact, spatial statistics is a special case of spatio-temporal statistics. One of our goals was to lay the foundation for serious consideration for spatio-temporal statistics as its own discipline. A more focused goal was to make the case for using spatio-temporal statistical models based on dynamical modelling of spatial processes, whenever possible.

5. Many reviews have also mentioned the use of four-colour in the book – green, blue and purple for, respectively, the data, process and parameter models, and red for posterior distribution. How has this use made the book more marketable?

When we approached John Wiley & Sons about the possibility of publishing this book, one of the most important things we wanted to see was a commitment to four-colour, given the importance of colour graphics to the depiction of spatio-temporal data. Wiley was very receptive to this vision. It was only in the process of writing that we realized how valuable it would be to indicate the data, process, and parameter levels of the hierarchical framework by the use of colour. We were very careful not to burden the readers with too much colour, but felt this, in addition to the figures, was a very pedagogical use of colour. We were really pleased with how well this turned out in the published version.

6. How would you compare this book to Statistics for Spatial Data?

Statistics for Spatial Data, or SSD, was an important book in that it was able to bring together what was before considered to be three seemingly disparate areas of spatial statistical analysis (geostatistics, areal data, and point processes) into a common notational and expositional framework. Although Statistics for Spatio-Temporal Data, SSTD, also comes at a good time in the evolution of the discipline, the research is probably in a bit more flux. Hence, the objective with SSTD is more about laying the critical framework (hierarchical modeling) and some of the key ideas, rather than being an exhaustive survey and unification of the existing literature. That being said, we worked hard to make SSTD very complete and up-to-date with regards to the existing literature in spatio-temporal statistics.

7. What is spatial data and how does it apply to our every-day lives?

Spatial data is referenced in some way to a location in physical space. More importantly, we are interested in data that are not only referenced by a spatial location, but also by a time index. Almost every data set falls in to this category, from basic meteorological measurements of temperature and wind, to satellite observations of total column ozone, to locations of IEDs in an evolving battlefield in a remote far-away location. In essence, we are surrounded by a swarm of data that is indexed in space and time. Our challenge is to find information in this swarm and to be able to use it to draw inference and make predictions.

8. Do you have any plans on writing together in the future? What will be your next book-length undertaking?

We are currently involved in a multi-million dollar grant with our colleague Scott Holan, funded by the US National Science Foundation and the US Census Bureau, to develop spatio-temporal methods for improving the usability and interpretability of the American Community Survey. We expect many publications to come from this work. At this point, we don’t have any plans for another book-length project, but one never knows where the research will take us!

9. How did you both begin to pursue a career in statistics and what was it that brought you to recognise statistics as a discipline in the first place?

Noel: I was always attracted to the applications of statistical methods to scientific problems. I received my PhD from Princeton University where I was greatly influenced by my advisor, Geoffrey Watson, and one of my teachers, John Tukey, who in their own way were committed to what I call Statistics in the Service of Science. In the last 10-20 years, our discipline of Statistics has also been called “The Science of Uncertainty.” I was very fortunate to teach Chris in my special topics class on Spatial Statistics, and we started to meet about his research plans. I remember research meetings with Chris that were enormously stimulating; only at the end of the meetings did I realize they had lasted a couple of hours!

Chris: I was trained originally as an atmospheric scientist. However, as everyone knows, there is a lot of uncertainty when it comes to weather forecasting! I was fortunate to be introduced to statistics and its power when I was a graduate student in meteorology, which led me to pursue graduate work in Statistics at Iowa State University. There, in addition to my exposure to geophysical fluid dynamics by Prof. Mike Chen, I was introduced to spatial statistics by Noel and hierarchical statistical modelling (experimentally at the time) by Prof. Mark Kaiser. These courses were extremely influential and very instrumental in forming my interest in bridging the gap between dynamics and statistical modelling of spatio-temporal processes.

10. As university professors, what do you think the future of teaching statistics will be? What do you think will be the upcoming challenges in engaging students?

In the last few years, there has been a clear shift in the expectations of students regarding electronic presentation and support materials. What used to be perfectly acceptable as derivation on a chalk (or white) board is now expected to be an electronic presentation. Let’s face it, in a world of internet gaming, Facebook, Twitter, etc., most students have shorter attention spans than in the past. They expect educational material to be presented in a similar style. For those of us who were classically trained academicians, this is an interesting and substantial challenge. However, we are both very interested in teaching and find it very rewarding, so are constantly trying to update our means of presentation.

11. Over the years, how has your teaching, consulting, and research motivated and influenced each other? Do you get research ideas from statistics and incorporate your ideas into your teaching?

Noel: Chris and I share ideas about teaching and the sort of spatial- and spatio-temporal- statistics material we can present with the least-demanding prerequisites. This is a challenge, since many students outside of Statistics would like to use spatial and spatio-temporal methodology. Making software available to people not trained to use it intelligently is a concern. We are looking for that sweet spot, where our courses and applied research are understandable to the largest possible student base.

Chris: I learned a great deal on how to teach spatial statistics from Noel when I was a student in his class (one of the best classes I ever had!). Since then I have developed a low-level applied spatial statistics class for undergraduates and graduate students outside of Statistics. This is very much a “hands on” class. I shared my laboratory computer assignments with Noel and he used a variant of them for a similar class he taught at Ohio State, which I then incorporated back into my class. In general, I always try to bring new research developments into my classes, whether they are in general data analysis, theory, or spatio-temporal statistics.

12. What do you think the most important recent developments in the field have been? What do you think will be the most exciting and productive areas of research in statistics during the next few years?

The development of Markov Chain Monte Carlo (MCMC) methods for Bayesian hierarchical models in the early 1990s has been one of the most important developments in Statistics in the last few decades. It is no coincidence that the surge in development of spatio-temporal methods in statistics has coincided with this development. In spatio-temporal statistics, the development of methods for high-dimensional data sets and processes will be critical. Furthermore, most of the development of dynamical methods for spatio-temporal processes has focused on linear processes. It is clear that most real-world phenomena are nonlinear and a substantial development of nonlinear spatio-temporal statistical methods is crucial for being able to model such processes.

13. What do you see as the greatest challenges facing the profession of statistics in the coming years?

At this point, the biggest challenge is going to be dealing with the huge volumes of information (data) that is available and converting this into knowledge. Statistics is a relatively young discipline, with most of the foundations appearing within the last 100 years. During most of that period, statisticians were concerned about inference when data samples were relatively small. These notions have been turned upside down in recent years with the preponderance of data that are available. One of the most exciting areas of spatio-temporal statistics is dealing with this curse of dimensionality by developing efficient low-dimensional representations of the underlying processes.

14. Are there people or events that have been influential in your careers?

Noel: I have already mentioned the influence of Geoffrey Watson and John Tukey, my professors at Princeton, and their deep understanding of science and uncertainty. I had a substantial foundation in Mathematics, and this gave me the tools needed to develop skills in statistical modelling. Writing down models in a suggestive notation is an art form we should all aspire to…I have developed the strong belief that “If you can’t write down the model, then you don’t understand it.” I have been fortunate in being a professor in US departments that had great graduate programs, and I have learned enormously from my students. Chris was an ideal student, and since he graduated he has developed a powerful research program that has been an important influence in my own research.

Chris: In addition to my PhD advisors, Noel and Mike Chen (in meteorology), who were enormously influential in my development, I was deeply influenced in Statistics by my postdoctoral advisor, Mark Berliner, who in some sense is the father of hierarchical modelling of environmental phenomena. I was very fortunate to come of “academic age” near the beginning of the MCMC era in modern statistics. The realization that these computational methods could be used in a general hierarchical Bayesian setting revolutionized modern statistics – including the development and implementation of spatio-temporal statistical methods.