IMS Bulletin 46(4)
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Happy 80Th, Ulf!
From SIAM News, Volume 37, Number 7, September 2004 Happy 80th, Ulf! My Grenander Number is two, a distinction that goes all the way back to 1958. In 1951, I wrote a paper on an aspect of the Bergman kernel function with Henry O. Pollak (who later became head of mathematics at the Bell Telephone Laboratories). In 1958, Ulf Grenander, Henry Pollak, and David Slepian wrote on the distribution of quadratic forms in normal varieties. Through my friendship with Henry, I learned of Ulf’s existence, and when Ulf came to Brown in 1966, I felt that this friendship would be passed on to me. And so it turned out. I had already read and appreciated the second of Ulf’s many books: On Toeplitz Forms and Their Applications (1958), written jointly with Gabor Szegö. Over the years, my wife and I have lived a block away from Ulf and “Pi” Grenander. (Pi = π = 3.14159...) We have known their children and their grandchildren. And I shouldn’t forget their many dogs. We have enjoyed their hospitality on numerous occasions, including graduations, weddings, and Lucia Day (December 13). We have visited with them in their summer home in Vastervik, Sweden. We have sailed with them around the nearby islands in the Baltic. And yet, despite the fact that our offices are separated by only a few feet, despite the fact that I have often pumped him for mathematical information and received mathematical wisdom in return, my Grenander Number has never been reduced to one. On May 7, 2004, about fifty people gathered in Warwick, Rhode Island, for an all-day celebration, Ulf Grenander from breakfast through dinner, in honor of Ulf’s 80th birthday. -
June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings for MATHEMATICS 2014 and Events Following a Very Generous Tions Open in Late 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 437 June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings FOR MATHEMATICS 2014 and Events Following a very generous tions open in late 2014. The prize Monday 16 June donation made by Professor may be awarded to either a single Midlands Regional Meeting, Loughborough Geoffrey Shephard, the London winner or jointly to collaborators. page 11 Mathematical Society will, in 2015, The mathematical contribution Friday 4 July introduce a new prize. The prize, to which an award will be made Graduate Student to be known as the Shephard must be published, though there Meeting, Prize will be awarded bienni- is no requirement that the pub- London ally. The award will be made to lication be in an LMS-published page 8 a mathematician (or mathemati- journal. Friday 4 July cians) based in the UK in recog- Professor Shephard himself is 1 Society Meeting nition of a specific contribution Professor of Mathematics at the Hardy Lecture to mathematics with a strong University of East Anglia whose London intuitive component which can be main fields of interest are in page 9 explained to those with little or convex geometry and tessella- Wednesday 9 July no knowledge of university math- tions. Professor Shephard is one LMS Popular Lectures ematics, though the work itself of the longest-standing members London may involve more advanced ideas. of the LMS, having given more page 17 The Society now actively en- than sixty years of membership. Tuesday 19 August courages members to consider The Society wishes to place on LMS Meeting and Reception nominees who could be put record its thanks for his support ICM 2014, Seoul forward for the award of a in the establishment of the new page 11 Shephard Prize when nomina- prize. -
Actuarial Science and Financial Mathematics Faqs
Department of Mathematics 250 Mathematics Building 231 W. 18th Avenue Columbus, OH 43210-1174 Actuarial Science and Financial Mathematics FAQs 1. What is the difference between a major in Actuarial Science and a major in Financial Math? Actuarial Science is the mathematical and statistical underpinning of the design, financing, and operation of all types of insurance, pension plans and benefit plans. Actuarial science prepares students for a career in the actuarial side of the insurance business and in actuarial consulting. Please see http://www.beanactuary.org/about/ for more information. Financial math track provides students with a foundation of the mathematics used in financial markets. It focuses on the pricing of the financial instruments (futures, options and other derivatives) and portfolio selection. Though there are job opportunities in financial institutions for students with an undergraduate degree, students in this track are encouraged to continue with graduate study in financial math, financial engineering, computational finance, or quantitative finance (they essentially mean the same thing). There are many professional master degree programs in this area. 2. How many students are currently majoring in actuarial science at Ohio State? We have close to 350 students in our program. 3. Are there any requirements to my actuarial major? If so, what are they? We place students into a pre-major when they switch or add this major. The major prerequisites and requirements can be found at https://math.osu.edu/undergrad/current- majors/requirements/actuarial. Students will also need to complete the College of Arts and Sciences General Education requirements. Students should meet with their academic advisor in the Math Advising Office or review the requirements online, https://math.osu.edu/undergrad/current-majors/requirements. -
Press Release
Press release 13 August 2014 Two Fields Medals 2014 awarded to ERC laureates The 2014 Fields Medals were awarded today to four outstanding mathematicians, of whom two are grantees of the European Research Council (ERC): Prof. Artur Avila (Brazil-France), an ERC Starting grant holder since 2010, and Prof. Martin Hairer (Austria) has been selected for funding under an ERC Consolidator grant in 2013. They received the prize respectively for their work on dynamical systems and probability, and on stochastic analysis. The other two laureates are Prof. Manjul Barghava (Canada-US) and Prof. Maryam Mirzakhani (Iran). The Medals were announced at the International Congress of Mathematicians (ICM) taking place from 13 – 21 August in Seoul, South Korea. On the occasion of the announcement, ERC President Prof. Jean-Pierre Bourguignon, a mathematician himself, said: “On behalf of the ERC Scientific Council, I would like to congratulate warmly all four Fields Medallists for their outstanding contributions to the field of mathematics. My special congratulations go to Artur Avila and Martin Hairer, who are both brilliant scientists supported by the ERC. We are happy to see that their remarkable talent in the endless frontiers of science has been recognised. The Fields Medals awarded today are also a sign that the ERC continues to identity and fund the most promising researchers across Europe; this is true not only in mathematics but in all scientific disciplines.” EU Commissioner for Research, Innovation and Science, Máire Geoghegan-Quinn, said: “I would like to congratulate the four laureates of the Fields Medal announced today. The Fields Medal, the highest international distinction for young mathematicians, is a well- deserved honour for hardworking and creative young researchers who push the boundaries of knowledge. -
Recent Challenges in Actuarial Science
ST09CH01_Embrechts ARjats.cls July 30, 2021 15:51 Annual Review of Statistics and Its Application Recent Challenges in Actuarial Science Paul Embrechts and Mario V. Wüthrich RiskLab, Department of Mathematics, ETH Zurich, Zurich, Switzerland, CH-8092; email: [email protected], [email protected] Annu. Rev. Stat. Appl. 2022. 9:1.1–1.22 Keywords The Annual Review of Statistics and Its Application is actuarial science, generalized linear models, life and non-life insurance, online at statistics.annualreviews.org neural networks, risk management, telematics data https://doi.org/10.1146/annurev-statistics-040120- 030244 Abstract Copyright © 2022 by Annual Reviews. For centuries, mathematicians and, later, statisticians, have found natural All rights reserved research and employment opportunities in the realm of insurance. By defini- tion, insurance offers financial cover against unforeseen events that involve an important component of randomness, and consequently, probability the- ory and mathematical statistics enter insurance modeling in a fundamental way. In recent years, a data deluge, coupled with ever-advancing information technology and the birth of data science, has revolutionized or is about to revolutionize most areas of actuarial science as well as insurance practice. We discuss parts of this evolution and, in the case of non-life insurance, show how a combination of classical tools from statistics, such as generalized lin- ear models and, e.g., neural networks contribute to better understanding and analysis of actuarial data. We further review areas of actuarial science where the cross fertilization between stochastics and insurance holds promise for both sides. Of course, the vastness of the field of insurance limits our choice of topics; we mainly focus on topics closer to our main areas of research. -
Department of Statistics and Actuarial Science Three Year Academic Plan 2004-2006 Approved by Department on 27 June 2006
Department of Statistics and Actuarial Science Three Year Academic Plan 2004-2006 Approved by Department on 27 June 2006 Chronology of Department Planning A. Achievement of Previous and Evaluation: Objectives and Recommendations: • May 2001: Formation of Department • Nov 2003: First Three-Year Plan (2003-6) The Department has achieved most of the • Mar 2005: External Review of Department objectives set out in its previous three-year • Mar 2006: Senate Approval of Recommen- plan, and has made a solid start at dations implementing the recommendations stemming • Jun 2006: Second Three-Year Plan (2007- from the 2005 external review. 9) Full, point-by-point assessments are Since its inception, the Department has provided in Appendices A and B. Of particular grown from 9 faculty positions to 20. Of these note, are the following: positions, 7 come with external or endowed New positions: The three-year plan called for funding. All faculty members are active in several academic appointments. As planned, research, and their collective record of we were able to hire two additional actuaries, external awards and funding is very strong. but the other target areas (a theoretician and a Over the last few years, the Department has lecturer) were not addressed. Instead, we took emerged as a leading Canadian center for advantage of our recognizable strengths to statistical teaching and research. A recruit very strong applicants for externally comparative analysis of NSERC grant funded and endowed positions. funding conducted for the recent external The plan also called for further half-positions in review ranked the Department very close to the general office and in the Statistical the best in the country. -
A Pattern Theoretic Approach
The Modelling of Biological Growth: a Pattern Theoretic Approach Nataliya Portman, Postdoctoral fellow McConnell Brain Imaging Centre Montreal Neurological Institute McGill University June 21, 2011 The Modelling of Biological Growth: a Pattern Theoretic Approach 2/ 47 Dedication This research work is dedicated to my PhD co-supervisor Dr. Ulf Grenander, the founder of Pattern Theory Division of Applied Mathematics, Brown University Providence, Rhode Island, USA. http://www.dam.brown.edu/ptg/ The Modelling of Biological Growth: a Pattern Theoretic Approach 3/ 47 Outline 1 Mathematical foundations of computational anatomy 2 Growth models in computational anatomy 3 A link between anatomical models and the GRID model 4 GRID view of growth on a fine time scale 5 GRID equation of growth on a coarse time scale (macroscopic growth law) 6 Image inference of growth properties of the Drosophila wing disc 7 Summary, concluding remarks and future perspectives 8 Current work The Modelling of Biological Growth: a Pattern Theoretic Approach 4/ 47 Mathematical foundations of computational anatomy Mathematical foundations of computational anatomy Computational anatomy1 focuses on the precise study of the biological variability of brain anatomy. D'Arcy Thompson laid out the vision of this discipline in his treatise \On Growth and Form" 2. In 1917 he wrote \In a very large part of morphology, our essential task lies in the comparison of related forms rather than in the precise definition of each; and the deformation of a complicated figure may be a phenomenon easy of comprehension, though the figure itself may be left unanalyzed and undefined." D'Arcy Thompson introduced the Method of Coordinates to accomplish the process of comparison. -
Actuarial Studies Within the Biometry and Statistics and Statistical Science Majors
Actuarial Studies within the Biometry and Statistics and Statistical Science majors An actuary is a business professional who analyzes the financial consequences of risk. Actuaries use mathematics, statistics and financial theory to study uncertain future events, especially those of concern to insurance and pension programs. They evaluate the likelihood of those events, design creative ways to reduce the likelihood and decrease the impact of adverse events that actually do occur. To be more specific, actuaries improve financial decision making by developing models to evaluate the current financial implications of uncertain future events. Actuaries are an important part of the management team of the companies that employ them. Their work requires a combination of strong analytical skills, business knowledge and understanding of human behavior to design and manage programs that control risk. No matter the source, actuary is consistently rated as one of the best jobs in America. US News and World Report, the Jobs Rated Almanac, CNN Money, and others all agree: few other occupations offer the combination of benefits that an actuarial career can offer. In almost every job satisfaction category, such as work environment, employment outlook, job security, growth opportunity, and salary (especially starting salary), a career as an actuary is hard to beat. Required courses for the Biometry and Statistics and Statistical Science majors Calculus I and II: MATH 1110 & 1120 Multivariable Calculus and Linear Algebra: MATH 2210 & 2220 or 2230 & 2240 -
Statistics and Actuarial Science 1
Statistics and Actuarial Science 1 STAT:3510/IGPI:3510 Biostatistics and STAT:4143/PSQF:4143 Statistics and Introduction to Statistical Methods. Students may not take STAT:3101/IGPI:3101 Introduction Actuarial Science to Mathematical Statistics II and STAT:4101/IGPI:4101 Mathematical Statistics II at the same time and get credit for both (nor go back to STAT:3101/IGPI:3101 after taking Chair STAT:4101/IGPI:4101). • Kung-Sik Chan Statistics Courses Director of Graduate Studies STAT:1000 First-Year Seminar 1 s.h. • Aixin Tan Small discussion class taught by a faculty member; topics Director of Undergraduate Studies, chosen by instructor; may include outside activities (e.g., films, lectures, performances, readings, visits to research Actuarial Science facilities). Requirements: first- or second-semester standing. • Elias S. Shiu STAT:1010 Statistics and Society 3 s.h. Director of Undergraduate Studies, Data Statistical ideas and their relevance to public policy, business, humanities, and the social, health, and physical Science sciences; focus on critical approach to statistical evidence. • Rhonda R. DeCook Requirements: one year of high school algebra or MATH:0100. GE: Quantitative or Formal Reasoning. Director of Undergraduate Studies, STAT:1015 Introduction to Data Science 3 s.h. Statistics Data collection, visualization, and wrangling; basics of • Rhonda R. DeCook probability and statistical inference; fundamentals of data learning including regression, classification, prediction, and Undergraduate majors: actuarial science (B.S.); statistics cross-validation; computing, learning, and reporting in the R (B.S.) environment; literate programming; reproducible research. Undergraduate minor: statistics Requirements: one year of high school algebra or MATH:0100. Graduate degrees: M.S. -
2018 Ulf Grenander Prize in Stochastic Theory and Modeling
AMS Prize Announcements FROM THE AMS SECRETARY 2018 Ulf Grenander Prize in Stochastic Theory and Modeling Judea Pearl was awarded the inaugural Ulf Grenander Prize in Stochastic Theory and Modeling at the 124th Annual Meeting of the AMS in San Diego, California, in January 2018. Citation belief propagation algorithm in Bayesian networks, which The 2018 Grenander Prize in recast the problem of computing posterior distributions Stochastic Theory and Modeling given evidence as a scheme for passing local messages is awarded to Judea Pearl for between network variables. Although exact computations the invention of a model-based through dynamic programming are possible, Pearl recog- approach to probabilistic and nized that in most problems of interest this would not be causal reasoning, for the discov- feasible, and in fact belief propagation turned out to be ery of innovative tools for infer- remarkably effective in many applications. ring these models from observa- Pearl’s primary goal in adopting Bayesian networks for tions, and for the development formulating structured models of complex systems was of novel computational methods his conviction that Bayesian networks would prove to be Judea Pearl for the practical applications of the right platform for addressing one of the most funda- these models. mental challenges to statistical modeling: the identifica- Grenander sought to develop general tools for con- tion of the conditional independencies among correlated structing realistic models of patterns in natural and variables that are induced by truly causal relationships. man-made systems. He believed in the power of rigorous In a series of papers in the 1990s, Pearl clearly showed mathematics and abstraction for the analysis of complex that statistical and causal notions are distinct and how models, statistical theory for efficient model inference, graphical causal models can provide a formal link between and the importance of computation for bridging theory causal quantities of interest and observed data. -
Norges Teknisk
ÆÇÊGEË ÌEÃÆÁËùÆAÌÍÊÎÁÌEÆËÃAÈEÄÁGE ÍÆÁÎEÊËÁÌEÌ E×ØiÑaØiÒg BÐÓÓd Îe××eÐ AÖea× iÒ ÍÐØÖa×ÓÙÒd ÁÑage× Í×iÒg a DefÓÖÑabÐe ÌeÑÔÐaØe ÅÓ deÐ bÝ ÇddÚaÖ ÀÙ×bÝ aÒd ÀaÚaÖd ÊÙe ÈÊEÈÊÁÆÌ ËÌAÌÁËÌÁCË ÆǺ ½7»¾¼¼½ ÁËËÆ: ¼8¼4¹9½7¿ ÆÇÊÏEGÁAÆ ÍÆÁÎEÊËÁÌY ÇF ËCÁEÆCE AÆD ÌECÀÆÇÄÇGY ÌÊÇÆDÀEÁŸ ÆÇÊÏAY Ìhi× ÖeÔ ÓÖØ ha× ÍÊÄ hØØÔ:»»ÛÛÛºÑaØhºÒØÒÙºÒÓ»ÔÖeÔÖiÒØ»×ØaØi×Øic×»¾¼¼½»Ë½7¹¾¼¼½ºÔ× ÀaÚaÖd ÊÙe ha× hÓÑeÔage: hØØÔ:»»ÛÛÛºÑaØhºÒØÒÙºÒÓ»hÖÙe E¹ÑaiÐ: hÖÙe@ÑaØhºÒØÒÙºÒÓ AddÖe××: DeÔaÖØÑeÒØ Óf ÅaØheÑaØicaÐ ËcieÒce׸ ÆÓÖÛegiaÒ ÍÒiÚeÖ×iØÝ Óf ËcieÒce aÒd ÌechÒÓÐÓgݸ ƹ749½ ÌÖÓÒdheiѸ ÆÓÖÛaݺ Estimating blood vessel areas in ultrasound images using a deformable template model Oddvar HUSBY and Havard˚ RUE Department of Mathematical Sciences Norwegian University of Science and Technology Norway October 9, 2001 Abstract We consider the problem of obtaining interval estimates of vessel areas from ul- trasound images of cross sections through the carotid artery. Robust and automatic estimates of the cross sectional area is of medical interest and of help in diagnosing atherosclerosis, which is caused by plaque deposits in the carotid artery. We approach this problem by using a deformable template to model the blood vessel outline, and use recent developments in ultrasound science to model the likelihood. We demonstrate that by using an explicit model for the outline, we can easily adjust for an important feature in the data: strong edge reflections called specular reflection. The posterior is challenging to explore, and naive standard MCMC algorithms simply converge to slowly. To obtain an efficient MCMC algorithm we make extensive use of computational efficient Gaus- sian Markov Random Fields, and use various block-sampling constructions that jointly update large parts of the model. -
The Pennsylvania State University the Graduate School Eberly College of Science
The Pennsylvania State University The Graduate School Eberly College of Science STUDIES ON THE LOCAL TIMES OF DISCRETE-TIME STOCHASTIC PROCESSES A Dissertation in Mathematics by Xiaofei Zheng c 2017 Xiaofei Zheng Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2017 The dissertation of Xiaofei Zheng was reviewed and approved∗ by the following: Manfred Denker Professor of Mathematics Dissertation Adviser Chair of Committee Alexei Novikov Professor of Mathematics Anna Mazzucato Professor of Mathematics Zhibiao Zhao Associate Professor of Statistics Svetlana Katok Professor of Mathematics Director of Graduate Studies ∗Signatures are on file in the Graduate School. Abstract This dissertation investigates the limit behaviors of the local times `(n; x) of the n Pn 1 partial sum fSng of stationary processes fφ ◦ T g: `(n; x) = i=1 fSi=xg. Under the conditional local limit theorem assumption: n kn BnP (Sn = knjT (·) = !) ! g(κ) if ! κ, P − a:s:; Bn we show that the limiting distribution of the local time is the Mittag-Leffler distri- bution when the state space of the stationary process is Z. The method is from the infinite ergodic theory of dynamic systems. We also prove that the discrete-time fractional Brownian motion (dfBm) admits a conditional local limit theorem and the local time of dfBm is closely related to but different from the Mittag-Leffler dis- tribution. We also prove that the local time of certain stationary processes satisfies an almost sure central limit theorem (ASCLT) under the additional assumption that the characteristic operator has a spectral gap. iii Table of Contents Acknowledgments vi Chapter 1 Introduction and Overview 1 1.0.1 Brownian local time .