Institute Of Statistical Mathematics Research Articles

GFN-xTB-Based Computations Provide Comprehensive Insights into Emulsion Radiation-Induced Graft Polymerization.

Invited for this month's cover are the collaborating groups of Dr. Ryohei Kakuchi and Ms. Kiho Matsubara at Gunma University, Japan, Prof. Kei Takahashi at Fukuoka Institute of Technology and The Institute of Statistical Mathematics, Japan, Prof. Takeshi Matsuda at Hannan University, Japan, Dr. Noriaki Seko and Dr. Yuji Ueki at National Institutes for Quantum Science and Technology, Japan. The cover picture shows the machine learning-based optimization and interpretation of radiation-induced graft polymerizations under emulsion conditions based on realistic information for monomers calculated by the state-of-the-art semiempirical method. More information can be found in the Research Article by Kiho Matsubara, Kei Takahashi, Ryohei Kakuchi, and co-workers.

A Conversation with Mary E. Thompson

Mary E. Thompson (née Beattie) was born September 9, 1944, in Winnipeg, Manitoba, Canada. She obtained a B.Sc. in Mathematics from the University of Toronto in 1965, and earned M.Sc. (1966) and Ph.D. (1969) degrees in Mathematics from the University of Illinois at Urbana-Champaign. She joined the Department of Statistics at the University of Waterloo as a Lecturer in 1969 and became an Assistant Professor in 1971. In 2004, she was awarded the honour of University Professor and in 2011 became Distinguished Professor Emerita at the University of Waterloo. She has served in many leadership roles including Chair of the Department of Statistics and Actuarial Science, Acting Dean of the Faculty of Mathematics, President of the Statistical Society of Canada (SSC) and Chair of the COPSS Presidents’ Award Committee. She chaired the Development Committee for the Canadian Statistical Sciences Institute (CANSSI) and was its founding Scientific Director. Thompson has received numerous honours and awards including the SSC’s Gold Medal, the Elizabeth L. Scott Award, the Waksberg Award of Survey Methodology and the Governor General’s Innovation Award. She is an elected member of the International Statistical Institute, an Honorary Member of the SSC and is a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, the Royal Society of Canada and the Fields Institute. Thompson has made fundamental contributions to several areas in statistics including sampling theory and the analysis of surveys. She is the author of two books in these areas: Theory of Sample Surveys (1997) and Sampling Theory and Practices (2020 with C. Wu). She has also made key contributions in estimation theory and stochastic processes. As the author of over 150 published, refereed papers, Thompson has influenced the theory and practice of statistics. The following conversation took place virtually in September 2022 with interviewer Rhonda J. Rosychuk of the University of Alberta.

A Conversation with Stephen Portnoy

Steve Portnoy was born in Kankakee, Illinois in 1942. He did his undergraduate studies in mathematics at Massachusetts Institute of Technology, and then earned a master’s degree and a Ph.D. degree from the statistics department at Stanford University in 1966 and 1969, respectively. Steve Portnoy has had a distinguished career and is widely recognized as a preeminent mathematical statistician. He has made pioneering and influential contributions in several areas in statistics, including asymptotic theory, robust statistics, quantile regression, and statistics in biology. He has published more than 100 research articles. He is a former co-editor of Journal of the American Statistical Association (Theory and Methods), an elected fellow of American Statistical Association (ASA), Institute of Mathematical Statistics (IMS) and American Association for the Advancement of Science (AAAS). Steve’s professional positions have included being on the faculty of the Department of Statistics at Harvard University and the University of Illinois at Urbana-Champaign for more than 30 years. He was a founding member of the Department of Statistics at the University of Illinois in 1985 and served as the division chair for the Statistics Program in the Mathematics department before the Statistics department was established.

Studying behaviours and attitudes towards science and technology

What makes research important is an important philosophical question that is a consideration for many researchers. Further important considerations are the public's perception of science and how an individual's perception of science and technology is shaped. These are some of the complex ideas that social scientist Dr Naoko Kato-Nitta, Department of Statistical Data Science, Institute of Statistical Mathematics, Japan, is exploring. She is working on a series of projects related to public perceptions and attitudes towards different scientific disciplines and fields. She hopes that answering such important questions will facilitate the creation of a science communication model for the public understanding of science. Kato-Nitta's research focuses on human behaviour and psychology and how it relates to issues at the interface of technology and society. A key question that she is seeking to answer from the standpoint of cultural capital is how the extent of the general public's participation in science communication can be determined. In the first research to connect social stratification theory and science communication research, Kato-Nitta divided the concept of Bourdieu's cultural capital into two sub-concepts: scientific and technical cultural capital and literary and artistic cultural capital. She went on to consider how these two types of cultural capital affect the exhibit-viewing behaviours of the general public.

A Conversation with Dennis Cook

Dennis Cook is a Full Professor, School of Statistics, at the University of Minnesota. He received his BS degree in Mathematics from Northern Montana College, and MS and PhD degrees in Statistics from Kansas State University. He has served as Chair of the Department of Applied Statistics, Director of the Statistical Center and Director of the School of Statistics, all at the University of Minnesota. His research areas include dimension reduction, linear and nonlinear regression, experimental design, statistical diagnostics, statistical graphics and population genetics. He has authored over 200 research articles and is author or co-author of two textbooks— An Introduction to Regression Graphics and Applied Regression Including Computing and Graphics—and three research monographs, Influence and Residuals in Regression, Regression Graphics: Ideas for Studying Regressions through Graphics and An Introduction to Envelopes: Dimension Reduction for Efficient Estimation in Multivariate Statistics. He has served as Associate Editor of the Journal of the American Statistical Association, The Journal of Quality Technology, Biometrika, Journal of the Royal Statistical Society and Statistica Sinica. He is a four-time recipient of the Jack Youden Prize for Best Expository Paper in Technometrics as well as the Frank Wilcoxon Award for Best Technical Paper. He received the 2005 COPSS Fisher Lecture and Award, and he is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics. The following conversation took place on March 22, 2019, following the banquet at the conference, “Cook’s Distance and Beyond: A Conference Celebrating the Contributions of R. Dennis Cook.” The interviewers were, Efstathia Bura (Effie), Bing Li, Lexin Li, Christopher Nachtsheim (Chris), Daniel Pena, Claude Messan Setodji and Robert Weiss (Rob).

Study on spacial-temporal analysis of ground surface temperature for global warming countermeasures

Extreme weather events can arrive unannounced and cause immense harm for communities. Especially in cities where many people live in close proximity, events like flash flooding, windstorms or even heat waves can cause property damage, overworking of the emergency infrastructure and death. Unfortunately, because climate change continues to alter weather patterns, from subtle local variations to changes in global factors like ocean currents, these events are occurring with increased frequency. There is a great need for accurate monitoring and prediction systems that can help forecast these catastrophes. Monitoring overall changes in the patterns of these events will also help governments and citizens better adapt and plan measures to protect themselves from climate change's inevitable impact. Professor Tomoko Matsui is an expert in the field of statistical spatial-temporal modelling. Matsui is heading up an international team of researchers at the Institute of Statistical Mathematics in Tokyo, Heriot-Watt University in UK and the National Institute for Environmental Studies in Tsukuba to find ways for using a variety of data including low-resolution surface meteorological observation, time-series measurements of ground surface temperature by high-resolution satellite and social media.

Improved $U$-tests for variance components in one-way random effects models

Based on a decomposition of a $U$-statistic, Nobre, Singer and Silvapulle (In Beyond Parametrics in Interdisciplinary Research, Festschrift to P.K. Sen (2008) 197–210 Institute of Mathematical Statistics) proposed a test for the hypothesis that the within-treatment variance component in a one-way random effects model is null, specially useful when very mild assumptions are imposed on the underlying distributions. We consider a bootstrap version of that $U$-test and evaluate its performance via simulation studies in different scenarios. The bootstrap $U$-test has better statistical properties than the original test even in small samples. Furthermore, it is easy to implement and has a low computational cost. We consider two examples with unbalanced small sample datasets, for illustrative purposes.

A Conversation with Grace Wahba

Grace Wahba (née Goldsmith, born August 3, 1934), I. J. Schoenberg-Hilldale Professor of Statistics at the University of Wisconsin-Madison (Emerita), is a pioneer in methods for smoothing noisy data. Her research combines theoretical analysis, computation and methodology motivated by innovative scientific applications. Best known for the development of generalized cross-validation (GCV), the connection between splines and Bayesian posterior estimates, and “Wahba’s problem,” she has developed methods with applications in demographic studies, machine learning, DNA microarrays, risk modeling, medical imaging and climate prediction. Grace grew up in the Washington, DC area and New Jersey, and graduated from Montclair High School. She was educated at Cornell (B.A. 1956), University of Maryland, College Park (M.A. 1962) and Stanford (Ph.D. 1966), and worked in industry for several years before receiving her doctorate in 1966 and settling in Madison in 1967. Although holding several visiting appointments, she has made Madison her home for over 50 years. She is the author of Spline Models for Observational Data which has garnered more than 8000 citations. Grace is treasured as an academic advisor and has mentored 39 Ph.D. students that have resulted in more than 330 academic descendants. She was elected to the United States National Academy of Sciences in 2000 and received an honorary degree of Doctor of Science from the University of Chicago in 2007. Wahba is a Fellow of several academic societies including the American Academy of Arts and Sciences, the American Association for the Advancement of Science, the American Statistical Association and the Institute of Mathematical Statistics. Over the years, she has received a selection of notable awards in the statistics community: R. A. Fisher Lectureship (2014), Gottfried E. Noether Senior Researcher Award (2009), Committee of Presidents of Statistical Societies Elizabeth Scott Award (1996) and the first Emanuel and Carol Parzen Prize for Statistical Innovation (1994).

A Conversation with Noel Cressie

Noel Cressie, FAA is Director of the Centre for Environmental Informatics in the National Institute for Applied Statistics Research Australia (NIASRA) and Distinguished Professor in the School of Mathematics and Applied Statistics at the University of Wollongong, Australia. He is also Adjunct Professor at the University of Missouri (USA), Affiliate of Org 398, Science Data Understanding, at NASA’s Jet Propulsion Laboratory (USA), and a member of the Science Team for NASA’s Orbiting Carbon Observatory-2 (OCO-2) satellite. Cressie was awarded a B.Sc. with First Class Honours in Mathematics in 1972 from the University of Western Australia, and an M.A. and Ph.D. in Statistics in 1973 and 1975, respectively, from Princeton University (USA). Two brief postdoctoral periods followed, at the Centre de Morphologie Mathématique, ENSMP, in Fontainebleau (France) from April 1975–September 1975, and at Imperial College, London (UK) from September 1975–January 1976. His past appointments have been at The Flinders University of South Australia from 1976–1983, at Iowa State University (USA) from 1983–1998, and at The Ohio State University (USA) from 1998–2012. He has authored or co-authored four books and more than 280 papers in peer-reviewed outlets, covering areas that include spatial and spatio-temporal statistics, environmental statistics, empirical-Bayesian and Bayesian methods including sequential design, goodness-of-fit, and remote sensing of the environment. Many of his papers also address important questions in the sciences. Cressie is a Fellow of the Australian Academy of Science, the American Statistical Association, the Institute of Mathematical Statistics, and the Spatial Econometrics Association, and he is an Elected Member of the International Statistical Institute. Noel Cressie’s refereed, unrefereed, and other publications are available at: https://niasra.uow.edu.au/cei/people/UOW232444.html.

A Conversation with Tom Louis

Thomas A. Louis received his BA in Mathematics from Dartmouth College in 1966 and his Ph.D. in Mathematical Statistics from Columbia University in 1972. He served as a NIH Postdoctoral Fellow at Imperial College, London, from 1972–1973 and has held faculty positions at Boston University, Harvard School of Public Health, the University of Minnesota and the Bloomberg School of Public Health at Johns Hopkins University. In addition, he served as a Senior Statistical Scientist at the RAND Corporation, and as Associate Director for Research and Methodology and Chief Scientist at the U.S. Census Bureau. Tom has served as President of both the Eastern North American Region of the International Biometric Society and as President of the International Biometric Society. He is a Fellow of the American Statistical Association, the American Association for the Advancement of Science and the Institute of Mathematical Statistics. As of January 2018, Tom is Emeritus Professor, Department of Biostatistics, Bloomberg School of Public Health, Johns Hopkins University. In addition to his many statistical accomplishments, Tom is a strong advocate for professional development and a life-long lover of time on the water.

Higher-Order Asymptotics and Its Application to Testing the Equality of the Examinee Ability Over Two Sets of Items.

In educational and psychological measurement, researchers and/or practitioners are often interested in examining whether the ability of an examinee is the same over two sets of items. Such problems can arise in measurement of change, detection of cheating on unproctored tests, erasure analysis, detection of item preknowledge, etc. Traditional frequentist approaches that are used in such problems include the Wald test, the likelihood ratio test, and the score test (e.g., Fischer, Appl Psychol Meas 27:3-26, 2003; Finkelman, Weiss, & Kim-Kang, Appl Psychol Meas 34:238-254, 2010; Glas & Dagohoy, Psychometrika 72:159-180, 2007; Guo & Drasgow, Int J Sel Assess 18:351-364, 2010; Klauer & Rettig, Br J Math Stat Psychol 43:193-206, 1990; Sinharay, J Educ Behav Stat 42:46-68, 2017). This paper shows that approaches based on higher-order asymptotics (e.g., Barndorff-Nielsen & Cox, Inference and asymptotics. Springer, London, 1994; Ghosh, Higher order asymptotics. Institute of Mathematical Statistics, Hayward, 1994) can also be used to test for the equality of the examinee ability over two sets of items. The modified signed likelihood ratio test (e.g., Barndorff-Nielsen, Biometrika 73:307-322, 1986) and the Lugannani-Rice approximation (Lugannani & Rice, Adv Appl Prob 12:475-490, 1980), both of which are based on higher-order asymptotics, are shown to provide some improvement over the traditional frequentist approaches in three simulations. Two real data examples are also provided.

Bayes linear analysis of risks in sequential optimal design problems

In a statistical or physical model, it is often the case that a set of design inputs must be selected in order to perform an experiment to collect data with which to update beliefs about a set of model parameters; frequently, the model also depends on a set of external variables which are unknown before the experiment is carried out, but which cannot be controlled. Sequential optimal design problems are concerned with selecting these design inputs in stages (at different points in time), such that the chosen design is optimal with respect to the set of possible outcomes of all future experiments which might be carried out. Such problems are computationally expensive. We consider the calculations which must be performed in order to solve a sequential design problem, and we propose a framework using Bayes linear emulators to approximate all difficult calculations which arise; these emulators are designed so that we can easily approximate expectations of the risk by integrating the emulator directly, and so that we can efficiently search the design input space for settings which may be optimal. We also consider how the structure of the design calculation can be exploited to improve the quality of the fitted emulators. Our framework is demonstrated through application to a simple linear modelling problem, and to a more complex airborne sensing problem, in which a sequence of aircraft flight paths must be designed so as to collect data which are informative for the locations of ground-based gas sources. © 2018, Institute of Mathematical Statistics. All rights reserved.

A Conversation with Lynne Billard

Lynne Billard was born in Toowomba, Australia. She earned her B.Sc. (Honors I) in 1966, and a Ph.D. degree in 1969, both from the University of New SouthWales, Australia. She is perhaps best known for her ground breaking research in the areas of HIV/AIDS and Symbolic Data Analysis. Broadly put, Professor Billard’s research interests include epidemic theory, stochastic processes, sequential analysis, time series analysis and symbolic data. She has written extensively in all these areas and more through numerous fundamental contributions. She has published more than 200 research papers in some of the leading international journals including Australian Journal of Statistics, Biometrika, Journal of American Statistical Association, Journal of Applied Probability, Journal of Royal Statistical Society, Journal of Time Series Analysis, Nature, Sequential Analysis, Statistical Science, Statistics in Medicine and Stochastic Processes and Their Applications, plus book chapters in a number of acclaimed edited volumes. Professor Billard has (co-)edited or (co-)authored eight prestigious books including her authoritative text (co-authored with E. Diday), Symbolic Data Analysis: Conceptual Statistics and Data Mining (2006) published byWiley. During the period 1969 through 1980, the career path took her to travel to University of Birmingham (U.K., 1969–1970), State University of New York at Buffalo (1971, 1974–1975), University ofWaterloo (Canada, 1971–1974), Stanford University (California, 1974), Florida State University at Tallahassee (1975–1980), Naval Postgraduate School (U.S.A., 1979), University of California (Berkeley, 1979), Imperial College (1986), Isaac Newton Institute, Cambridge (1993), and other prestigious places. She had joined the Department of Statistics at Florida State University as an Associate Professor in 1975 and during 1976–1978 she served as the Associate Head there. She became a Professor at Florida State in 1980 but went on leave to visit the Department of Computer Science and Statistics at University of Georgia, Athens. She joined the same department in Georgia permanently as Professor of Statistics and Head in 1980. When the Department of Statistics was formed in Georgia under Professor Billard’s leadership, she became its Professor and Head (1984–1989). Since 1992, she has held the most prestigious and coveted position, the University Professor, in the University of Georgia. She served as an Associate Editor for numerous journals including the Journal of American Statistical Association and Statistical Analysis and Data Mining. All her life, she has served extensively by holding high-level offices as well as memberships of both national and international committees at several scholarly international societies including the American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), International Biometrics Society (IBS) and Eastern North American Region (ENAR), Bernoulli Society and the International Statistical Institute (ISI). For example, Professor Billard was elected President of ENAR (1985), International Vice President (1993, 1996) and International President (1994, 1995) of IBS and President of ASA (1996). She has earned many honors and awards, including Fellow of the IMS (1988), Fellow of the ASA (1980), Fellow of the American Association for the Advancement of Science (2001) and elected membership in the ISI (1980). Professor Billard received several prestigious awards including the S. S. Wilks Medal (1999) of the ASA. Its citation read, “For significant contributions to the theory and methodology of statistics and the advancement of scientific knowledge in a variety of fields, especially in the area of HIV/AIDS; for effective leadership on issues of public interest, particularly with respect to the decennial census; for energetic professional service nationally and internationally; and for influential dedication to the statistical education of both statisticians and the public at large.” She was honored by the Founders Award (2003) from the ASA. She received the Committee of Presidents of Statistical Societies (COPSS) Elizabeth Scott Award (2008) and FN David Award (2013), as well as the Janet L Norwood Award (2011). In 2015, she was installed as an Honorary Member of the Statistical Society of Slovenia. Professor Billard travels extensively to scientific conferences as an invited participant, works harder than many half her age, and continues to inspire through her writings and uniquely affectionate presence. The following conversation began August 1, 2011, at the Joint Statistical Meetings held in Miami, Florida.

A Review and Comparison of Age–Period–Cohort Models for Cancer Incidence

Age-period-cohort models have been used to examine and forecast cancer incidence and mortality for over three decades. However, the fitting and interpretation of these models requires great care because of the well-known identifiability problem that exists; given any two of age, period, and cohort, the third is determined. In this paper, we review the identifiability problem and models that have been proposed for analysis, from both frequentist and Bayesian standpoints. A number of recent analyses that use age-period-cohort models are described and critiqued before data on cancer incidence inWashington State are analyzed with various models, including a new Bayesian approach based on an identifiable parameterization. © Institute of Mathematical Statistics, 2016.

Dynamic changepoint detection in count time series: a particle filter approach

ABSTRACTWe study Bayesian dynamic models for detecting changepoints in count time series that present structural breaks. As the inferential approach, we develop a parameter learning version of the algorithm proposed by Chopin [Chopin N. Dynamic detection of changepoints in long time series. Annals of the Institute of Statistical Mathematics 2007;59:349–366.], called the Chopin filter with parameter learning, which allows us to estimate the static parameters in the model. In this extension, the static parameters are addressed by using the kernel smoothing approximations proposed by Liu and West [Liu J, West M. Combined parameters and state estimation in simulation-based filtering. In: Doucet A, de Freitas N, Gordon N, editors. Sequential Monte Carlo methods in practice. New York: Springer-Verlag; 2001]. The proposed methodology is then applied to both simulated and real data sets and the time series models include distributions that allow for overdispersion and/or zero inflation. Since our procedure is general, robust and naturally adaptive because the particle filter approach does not require restrictive specifications to ensure its validity and effectiveness, we believe it is a valuable alternative for dealing with the problem of detecting changepoints in count time series. The proposed methodology is also suitable for count time series with no changepoints and for independent count data.

Exploiting the Feller Coupling for the Ewens Sampling Formula

This is the final version of the article. It first appeared from the Institute of Mathematical Statistics via http://dx.doi.org/10.1214/15-STS537

Lower and upper bounds on the variances of spacings

For classic i.i.d. samples with an arbitrary nondegenerate and finite variance distribution, Papadatos (1995, Annals of the Institute of Statistical Mathematics, 47, 185–193) presented sharp lower and upper bounds on the variances of order statistics, expressed in population variance units. We provide here analogous results for spacings. Also, we describe the parent distributions which attain the bounds.

Scientific Endeavors of A.M. Mathai: An Appraisal on the Occasion of his Eightieth Birthday, 28 April 2015

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada. He is currently the Director of the Centre for Mathematical and Statistical Sciences India. His research contributions cover a wide spectrum of topics in mathematics, statistics, physics, astronomy, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, and a member of the International Statistical Institute. He is a founder of the Canadian Journal of Statistics and the Statistical Society of Canada. He was instrumental in the implementation of the United Nations Basic Space Science Initiative (1991–2012). This paper highlights research results of A.M. Mathai in the period of time from 1962 to 2015. He published over 300 research papers and over 25 books.

Trust of Nations: Looking for More Universal Values for Interpersonal and International Relationships

The objective of this study is to review past research on people’s sense of trust as reflected in the data from longitudinal and cross-national comparative surveys by the Institute of Statistical Mathematics. First, I explain some history of our survey research. Second, I give a brief review of the studies on sense of trust. Third, I summarize some aspects of the fundamental social values of the Japanese and their sense of interpersonal trust as identified in our Japanese National Character Survey. Fourth, I present a crossnational comparative analysis of interpersonal trust and institutional trust, including the Seven Country Survey (Japan, the USA, and five European countries) (1987–1993), Japanese immigrant surveys, the East Asia Values Survey (2002–2005), the Pacific-Rim Values Survey (2004–2009), and the Asia-Pacific Values Survey (2010–2014). To overcome the limitations of the studies based mostly on the items of the General Social Survey or the World Values Survey, I explore more basic social values on human bonds that may underlie people’s sense of trust beyond differences in countries or time. The final section presents some comments for our future research.

The Asia-Pacific Values Survey 2010–2014: Cultural Manifold Analysis of National Character

The Institute of Statistical Mathematics has been conducting a longitudinal survey on Japanese national character since 1953. From 1971, this survey was extended to include cross-national comparative surveys and people of Japanese ancestry in Hawaii, the West Coast of the United States, and Brazil. The cross-national survey primarily focuses on comparing social values, ways of thinking and feeling, and other relevant characteristics of people from various nations. This study investigates conditions under which meaningful cross-national comparability of social survey data is guaranteed, despite differences in languages and statistical sampling methods. Over the past 14 years, focusing on Asian countries, we have carried out the East Asia Values Survey (2002–2005), the Pacific Rim Values Survey (2004–2009), and the Asia-Pacific Values Survey (2010–2014). In this introductory paper to the special issue, we discuss the development of our research paradigm, termed cultural manifold analysis (CULMAN), and provide an overview of our past surveys. We conclude with comments on our future research.