Geometry Driven Statistics (eBook)

Ian L. Dryden, John T. Kent (Herausgeber)

eBook Download: EPUB

2015
John Wiley & Sons (Verlag)
978-1-118-86660-3 (ISBN)

Infos

A timely collection of advanced, original material in the area of statistical methodology motivated by geometric problems, dedicated to the influential work of Kanti V. Mardia

This volume celebrates Kanti V. Mardia's long and influential career in statistics. A common theme unifying much of Mardia’s work is the importance of geometry in statistics, and to highlight the areas emphasized in his research this book brings together 16 contributions from high-profile researchers in the field.

Geometry Driven Statistics covers a wide range of application areas including directional data, shape analysis, spatial data, climate science, fingerprints, image analysis, computer vision and bioinformatics. The book will appeal to statisticians and others with an interest in data motivated by geometric considerations.

Summarizing the state of the art, examining some new developments and presenting a vision for the future, Geometry Driven Statistics will enable the reader to broaden knowledge of important research areas in statistics and gain a new appreciation of the work and influence of Kanti V. Mardia.

Autor

Ian L. Dryden, University of Nottingham, UK John T. Kent, University of Leeds, UK

Textauszug

Chapter 1
A Conversation with Kanti Mardia

Nitis Mukhopadhyay

Department of Statistics, University of Connecticut, Storrs, CT, USA

This paper originally appeared in Statistical Science 2002, Vol. 17, No. 1, 113–148.

Kantilal Vardichand Mardia was born on April 3, 1935, in Sirohi, Rajasthan, India. He earned his B.Sc. degree in mathematics from Ismail Yusuf College—University of Bombay, in 1955, M.Sc. degrees in statistics and in pure mathematics from University of Bombay in 1957 and University of Poona in 1961, respectively, and Ph.D. degrees in statistics from the University of Rajasthan and the University of Newcastle, respectively, in 1965 and 1967. For significant contributions in statistics, he was awarded a D.Sc. degree from the University of Newcastle in 1973. He started his career as an Assistant Lecturer in the Institute of Science, Bombay and went to Newcastle as a Commonwealth Scholar. After receiving the Ph.D. degree from Newcastle, he joined the University of Hull as a lecturer in statistics in 1967, later becoming a reader in statistics in 1971. He was appointed a Chair Professor in Applied Statistics at the University of Leeds in 1973 and was the Head of the Department of Statistics during 1976–1993, and again from 1997 to the present. Professor Mardia has made pioneering contributions in many areas of statistics including multivariate analysis, directional data analysis, shape analysis, and spatial statistics. He has been credited for path-breaking contributions in geostatistics, imaging, machine vision, tracking, and spatio-temporal modeling, to name a few. He was instrumental in the founding of the Center of Medical Imaging Research in Leeds and he holds the position of a joint director of this internationally eminent center. He has pushed hard in creating exchange programs between Leeds and other scholarly centers such as the University of Granada, Spain, and the Indian Statistical Institute, Calcutta. He has written several scholarly books and edited conference proceedings and other special volumes. But perhaps he is best known for his books: Multivariate Analysis (coauthored with John Kent and John Bibby, 1979, Academic Press), Statistics of Directional Data (second edition with Peter Jupp, 1999, Wiley) and Statistical Shape Analysis (coauthored with Ian Dryden, 1998, Wiley). The conferences and workshops he has been organizing in Leeds for a number of years have had significant impacts on statistics and its interface with IT (information technology). He is dynamic and his sense of humor is unmistakable. He is a world traveler. Among other places, he has visited Princeton University, the University of Michigan, Harvard University, the University of Granada, Penn State and the University of Connecticut. He has given keynote addresses and invited lectures in international conferences on numerous occasions. He has been on the editorial board of statistical, as well as image related, journals including the IEEE Transactions on Pattern Analysis and Machine Intelligence, Journal of Environmental and Ecological Statistics, Journal of Statistical Planning and Inference and Journal of Applied Statistics. He has been elected a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and a Fellow of the American Dermatoglyphic Association. He is also an elected member of the International Statistical Institute and a Senior Member of IEEE. Professor Mardia retired on September 30, 2000 to take a full-time post as Senior Research Professor at Leeds—a new position especially created for him.

In April, 1999, Professor Kanti V. Mardia was invited to the University of Connecticut as a short-term guest professor for four weeks. This conversation began on Monday, April 19, 1999 in Nitis Mukhopadhyay's office in the Department of Statistics, University of Connecticut, Storrs.

1.1 Family background

Mukhopadhyay: Kanti, shall we start at the origin, so to speak? Where were you born?

Mardia: I was born in Sirohi on April 3, 1935. Sirohi, was the capital of the Sirohi State about ten thousand square miles in area, in Rajasthan, before India's independence. Subsequently, the Sirohi State became the Sirohi district. Sirohi is situated about four hundred miles east of Bombay. One of the greatest wonders near my place of birth has been the hill station, Mount Abu. It has one of the finest Jain temples, Delwara, with gorgeous Indian architecture from the eleventh century. The exquisite details are all meticulously hand-curved on marble, without parallels anywhere else in India. Those shapes and formations on the ceiling and columns with intricate details influenced me even when I was small child. Much later in my life, some of those incredible shapes made deeper and more tangible impacts on my research career.

Mukhopadhyay: Please tell me about your parents.

Mardia: I come from a business family. My father's and mother's names are, respectively, Vardichand and Sanghari. My father inherited the business of moneylending from my grandfather and he had a pawnbroker's shop in Bombay. My grandfather started with practically nothing but through his business acumen acquired a large fortune.

But, my father had to live through some tragedies. He lost his father, two brothers and their families in the span of one year in an epidemic. Due to the spread of some severe unknown disease in that particular area, many in his family perished. My father, about sixteen, was practically the lone survivor in his family.

Figure 1.1 Kanti Mardia on his uncle's lap, Bombay, 1940.

Figure 1.2 Ceiling from Jain Temple at Mount Abu (Rajasthan), Sirohi District. Original in white marble with tendrils circling in a fractal form, 1031 AD.

Mukhopadhyay: How did this episode affect your father and the family?

Mardia: It had a devastating effect. My father started taking life very philosophically and decided to take everything easy. His whole perspective of life changed. He passed on the family businesses to my uncles. One uncle was a compulsive gambler who piled up huge debts. Eventually, many of the family businesses and other assets (e.g., several buildings and movie theaters in and around Bombay) were lost as loan payments on those debts. By the time I turned ten, our family had already slipped down from a very rich status and joined the upper middle class.

Mukhopadhyay: What about your mother's side of the family?

Mardia: My maternal grandfather was a lawyer and writer. He was an original thinker. He wrote a number of novels. Any writing skills I may have, I probably inherited from him.

Mukhopadhyay: How about your brothers and sisters?

Mardia: I have four brothers and one sister. It is a large family. I am the one in the middle, a kind of the “median,” a robust estimator. (Laughs.)

I became the first college graduate in the family. My brother Mangesh Kumarji looked after the family-run businesses. He earned real money to support the family while I had to study for my degrees! (Laughs.)

Mukhopadhyay: Was any of your siblings mathematically oriented?

Mardia: My younger brother Babu followed my footsteps and got a masters degree in pure mathematics. He is an Associate professor of Mathematics in Rajasthan University, Udaipur, India. During my childhood and school days, we lived in Sirohi as well as in Bombay, a major city center for all the businesses. We had to shuttle between these two places.

1.2 School days

Mukhopadhyay: Where and how did your schooling begin?

Mardia: In kindergarten, we learned numbers and even simple fractions. For example, at the age of four or five, we learned the concept of what is one-half of ten or one-quarter of eight! We had to memorize such multiplication tables and the teachers were very strict. We also had to learn to speak and write in Hindi, but this had to be mastered with the Rajasthani script and dialect, even though those styles were practically dead by then. It did feel like I was mastering a foreign language. This was on top of learning English.

Mukhopadhyay: Did you happen to have some inspiring teachers?

Mardia: In my time, there was only one high school in Sirohi, which I had to attend. Neither the teachers nor the curriculum had any flexibility and I did not like most of the subjects very much, except for mathematics. In the lower grades, we had a mathematics teacher who hailed from Ajmer, another part of Rajasthan, and he had an interesting habit. He used to assign challenging mathematical puzzles to the class and gave small prizes to whoever could solve the puzzles first. I was pretty good in solving such mathematical puzzles and won many prizes along the way. This math teacher had a big influence on me. I also enjoyed plane Euclidean geometry very much. I went through these constructions and proofs of theorems based on axioms. However, I have to confess that I preferred algebraic derivations and proofs with equations to the geometry-based arguments. (Laughs.)

Mukhopadhyay: (Laughs) Kanti, in quiet moments, sometimes you probably think what an irony of life that was!

Mardia: (Laughs) Nitis, you are right. Later in life, “geometry” became my mantra. What an irony indeed! I was not very interested nor considered particularly bright by others in nonmathematical subjects. I...

Produkt-Details

• Erscheint lt. Verlag: 3.9.2015
• Reihe/Serie: Wiley Series in Probability and Statistics
• Reihe/Serie: Wiley Series in Probability and Statistics
• Reihe/Serie: Wiley Series in Probability and Statistics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Angewandte Wahrscheinlichkeitsrechnung u. Statistik • Applied Probability & Statistics • Bayesian Statistics • Bioinformatics • biometrics • Biometrie • Computational Statistics • Directional Statistics • Image Analysis • interdisciplinary statistics • Multivariate Analyse • multivariate analysis • shape analysis • spatial analysis • spatial-temporal analysis • Statistics • Statistik
• ISBN-10: 1-118-86660-6 / 1118866606
• ISBN-13: 978-1-118-86660-3 / 9781118866603