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A Computer Algebra System for R: Macaulay2 and the M2r Package
A computer algebra system for R: Macaulay2 and the m2r package David Kahle∗1, Christopher O'Neilly2, and Jeff Sommarsz3 1Department of Statistical Science, Baylor University 2Department of Mathematics, University of California, Davis 3Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago Abstract Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to bear on statistical problems. Now over two decades old, algebraic statistics has applications in a wide range of theoretical and applied statistical domains. Nevertheless, algebraic statistical methods are still not mainstream, mostly due to a lack of easy off-the-shelf imple- mentations. In this article we debut m2r, an R package that connects R to Macaulay2 through a persistent back-end socket connection running locally or on a cloud server. Topics range from basic use of m2r to applications and design philosophy. 1 Introduction Algebra, a branch of mathematics concerned with abstraction, structure, and symmetry, has a long history of applications in statistics. For example, Pearson's early work on method of moments estimation in mixture models ultimately involved systems of polynomial equations that he painstakingly and remarkably solved by hand (Pearson, 1894; Am´endolaet al., 2016). Fisher's work in design was strongly algebraic and combinato- rial, focusing on topics such as Latin squares (Fisher, 1934). Invariance and equivariance continue to form a major pillar of mathematical statistics through the lens of location-scale families (Pitman, 1939; Bondesson, 1983; Lehmann and Romano, 2005). -
Algebraic Statistics Tutorial I Alleles Are in Hardy-Weinberg Equilibrium, the Genotype Frequencies Are
Example: Hardy-Weinberg Equilibrium Suppose a gene has two alleles, a and A. If allele a occurs in the population with frequency θ (and A with frequency 1 − θ) and these Algebraic Statistics Tutorial I alleles are in Hardy-Weinberg equilibrium, the genotype frequencies are P(X = aa)=θ2, P(X = aA)=2θ(1 − θ), P(X = AA)=(1 − θ)2 Seth Sullivant The model of Hardy-Weinberg equilibrium is the set North Carolina State University July 22, 2012 2 2 M = θ , 2θ(1 − θ), (1 − θ) | θ ∈ [0, 1] ⊂ ∆3 2 I(M)=paa+paA+pAA−1, paA−4paapAA Seth Sullivant (NCSU) Algebraic Statistics July 22, 2012 1 / 32 Seth Sullivant (NCSU) Algebraic Statistics July 22, 2012 2 / 32 Main Point of This Tutorial Phylogenetics Problem Given a collection of species, find the tree that explains their history. Many statistical models are described by (semi)-algebraic constraints on a natural parameter space. Generators of the vanishing ideal can be useful for constructing algorithms or analyzing properties of statistical model. Two Examples Phylogenetic Algebraic Geometry Sampling Contingency Tables Data consists of aligned DNA sequences from homologous genes Human: ...ACCGTGCAACGTGAACGA... Chimp: ...ACCTTGGAAGGTAAACGA... Gorilla: ...ACCGTGCAACGTAAACTA... Seth Sullivant (NCSU) Algebraic Statistics July 22, 2012 3 / 32 Seth Sullivant (NCSU) Algebraic Statistics July 22, 2012 4 / 32 Model-Based Phylogenetics Phylogenetic Models Use a probabilistic model of mutations Assuming site independence: Parameters for the model are the combinatorial tree T , and rate Phylogenetic Model is a latent class graphical model parameters for mutations on each edge Vertex v ∈ T gives a random variable Xv ∈ {A, C, G, T} Models give a probability for observing a particular aligned All random variables corresponding to internal nodes are latent collection of DNA sequences ACCGTGCAACGTGAACGA Human: X1 X2 X3 Chimp: ACGTTGCAAGGTAAACGA Gorilla: ACCGTGCAACGTAAACTA Y 2 Assuming site independence, data is summarized by empirical Y 1 distribution of columns in the alignment. -
BERNOULLI NEWS, Vol 24 No 2 (2017)
Vol. 24 (2), November 2017 Published twice per year by the Bernoulli Society ISSN 1360–6727 CONTENTS News from the Bernoulli A VIEW FROM THE PRESIDENT Society p. 1 Awards and Prizes p. 2 New Executive Members in the Bernoulli Society p. 3 Articles and Letters On Bayesian Measures for Some Statistical Inverse Problems with Partial Differential Equations p. 5 Obituary Alastair Scott p. 10 Past Conferences, Susan A. Murphy receives the Bernoulli Book from Sara van de Geer during the General Assembly of the Bernoulli Society ISI World Congress in Marrakech, Morocco. Meetings and Workshops p. 11 Dear Members of the Bernoulli Society, Next Conferences, Meetings and Workshops It is an honor to assume the role of Bernoulli Society president, particularly be- cause this is a very exciting time to be a statistician or probabilist! As all of us have and Calendar of Events become, ever-more acutely aware, the role of data in society and in science is dramat- p. 13 ically changing. Many new challenges are due to the complex, and vast amounts of, data resulting from the development of new data collection tools such as wearable Book Reviews sensors in clothing, on eyeglasses, in toothbrushes and most commonly on our phones. Indeed there are now wearable radar sensors that provide data that might be used Editor to improve the safety of bicyclists or help visually impaired individuals gain greater MIGUEL DE CARVALHO independence. There are also wearable respiratory sensors that provide data that School of Mathematics could be used to help us investigate the impact of dietary and exercise regimens, or THE UNIVERSITY of EDINBURGH EDINBURGH, UK identify nutritional imbalances. -
IMS Grace Wahba Award and Lecture
Volume 50 • Issue 4 IMS Bulletin June/July 2021 IMS Grace Wahba Award and Lecture The IMS is pleased to announce the creation of a new award and lecture, to honor CONTENTS Grace Wahba’s monumental contributions to statistics and science. These include her 1 New IMS Grace Wahba Award pioneering and influential work in mathematical statistics, machine learning and opti- and Lecture mization; broad and career-long interdisciplinary collaborations that have had a sig- 2 Members’ news : Kenneth nificant impact in epidemiology, bioinformatics and climate sciences; and outstanding Lange, Kerrie Mengersen, Nan mentoring during her 51-year career as an educator. The inaugural Wahba award and Laird, Daniel Remenik, Richard lecture is planned for the 2022 IMS annual meeting in London, then annually at JSM. Samworth Grace Wahba is one of the outstanding statisticians of our age. She has transformed 4 Grace Wahba: profile the fields of mathematical statistics and applied statistics. Wahba’s RKHS theory plays a central role in nonparametric smoothing and splines, and its importance is widely 7 Caucus for Women in recognized. In addition, Wahba’s contributions Statistics 50th anniversary straddle the boundary between statistics and 8 IMS Travel Award winners optimization, and have led to fundamental break- 9 Radu’s Rides: Notes to my Past throughs in machine learning for solving problems Self arising in prediction, classification and cross-vali- dation. She has paved a foundation for connecting 10 Previews: Nancy Zhang, Ilmun Kim theory and practice of function estimation, and has developed, along with her students, unified 11 Nominate IMS Lecturers estimation methods, scalable algorithms and 12 IMS Fellows 2021 standard software toolboxes that have made regu- 16 Recent papers: AIHP and larization approaches widely applicable to solving Observational Studies complex problems in modern science discovery Grace Wahba and technology innovation. -
Blueprint Staff Magazine for the University of Oxford | September 2016
blueprint Staff magazine for the University of Oxford | September 2016 Chemistry’s organic growth | Secrets of successful spelling | Oxford time News in brief u Oxford has topped the Times Higher research fellow at the college, set off at 6.30am Education World University Rankings for and arrived at Homerton, Harris Manchester’s 2016–17 – the first time in the 13-year history of twin college, in the afternoon. OxfordUniversity Images/Rob Judges the rankings that a UK institution has secured the top spot. The rankings judge research-intensive u The University’s phone system is being universities across five areas: teaching, research, replaced by a new service called Chorus. citations, international outlook and knowledge The service is being rolled out on a building- transfer. In total UK institutions took 91 of the by-building basis between autumn 2016 and 980 places, with the University of Cambridge spring 2018. Chorus will deliver replacement (fourth) and Imperial College London (eighth) phones together with access to a web portal, also making the top ten. which will provide additional functionality such as managing your voicemail, accessing u The University and local NHS partners have your call history, and sending and receiving won £126.5m to support medical research. instant messages. Details at https://projects.it. The money, from the National Institute for ox.ac.uk/icp. Health Research, includes £113.7m for the existing University of Oxford/Oxford University u The University has opened a new nursery Hospitals Biomedical Research Centre, and on the Old Road Campus in Headington, £12.8m for a new Biomedical Research Centre bringing the total number of University-owned specialising in mental health and dementia, nurseries to five. -
Algebraic Statistics of Design of Experiments
Thammasat University, Bangkok Algebraic Statistics of Design of Experiments Giovanni Pistone Bangkok, March 14 2012 The talk 1. A short history of AS from a personal perspective. See a longer account by E. Riccomagno in • E. Riccomagno, Metrika 69(2-3), 397 (2009), ISSN 0026-1335, http://dx.doi.org/10.1007/s00184-008-0222-3. 2. The algebraic description of a designed experiment. I use the tutorial by M.P. Rogantin: • http://www.dima.unige.it/~rogantin/AS-DOE.pdf 3. Topics from the theory, cfr. the course teached by E. Riccomagno, H. Wynn and Hugo Maruri-Aguilar in 2009 at the Second de Brun Workshop in Galway: • http://hamilton.nuigalway.ie/DeBrunCentre/ SecondWorkshop/online.html. CIMPA Ecole \Statistique", 1980 `aNice (France) Sumate Sompakdee, GP, and Chantaluck Na Pombejra First paper People • Roberto Fontana, DISMA Politecnico di Torino. • Fabio Rapallo, Universit`adel Piemonte Orientale. • Eva Riccomagno DIMA Universit`adi Genova. • Maria Piera Rogantin, DIMA, Universit`adi Genova. • Henry P. Wynn, LSE London. AS and DoE: old biblio and state of the art Beginning of AS in DoE • G. Pistone, H.P. Wynn, Biometrika 83(3), 653 (1996), ISSN 0006-3444 • L. Robbiano, Gr¨obnerBases and Statistics, in Gr¨obnerBases and Applications (Proc. of the Conf. 33 Years of Gr¨obnerBases), edited by B. Buchberger, F. Winkler (Cambridge University Press, 1998), Vol. 251 of London Mathematical Society Lecture Notes, pp. 179{204 • R. Fontana, G. Pistone, M. Rogantin, Journal of Statistical Planning and Inference 87(1), 149 (2000), ISSN 0378-3758 • G. Pistone, E. Riccomagno, H.P. Wynn, Algebraic statistics: Computational commutative algebra in statistics, Vol. -
978-961-293-071-4.Pdf PUBLIC LECTURES 53
CONTENTS 8th European Congress of Mathematics 20–26 June 2021 • Portorož, Slovenia PLENARY SPEAKERS 1 Presentation of Plenary, Invited, Public, Abel and Prize Speakers at the 8ECM Edited by INVITED SPEAKERS 11 Nino Bašic´ Ademir Hujdurovic´ Klavdija Kutnar THE EMS PRIZES 33 Tomaž Pisanski Vito Vitrih THE FELIX KLEIN PRIZE 43 Published by University of Primorska Press THE OTTO NEUGEBAUER PRIZE 45 Koper, Slovenia • www.hippocampus.si © 2021 University of Primorska ABEL LECTURE 49 Electronic Edition https://www.hippocampus.si/ISBN/978-961-293-071-4.pdf PUBLIC LECTURES 53 https://www.hippocampus.si/ISBN/978-961-293-072-1/index.html https://doi.org/10.26493/978-961-293-071-4 Kataložni zapis o publikaciji (CIP) pripravili v Narodni in univerzitetni knjižnici v Ljubljani COBISS.SI-ID = 65201411 ISBN 978-961-293-071-4 (pdf) ISBN 978-961-293-072-1 (html) PLENARY SPEAKERS 8th European Congress of Mathematics Plenary Speakers Peter Bühlmann Nirenberg, from the Courant Institute, New York University, 1994. Following his PhD, he has held the positions of Member of the Institute for Advanced ETH Zürich Study, Princeton, 1994–95; Habilitation à diriger des recherches, Université Pierre et Marie Curie-Paris VI, 1998; Harrington Faculty Fellow, The University of Texas at Austin, 2001–02; and Tenure Associate Professor, The University Biosketch of Texas at Austin, 2002–03. Since 2003, he has been an ICREA Research Peter Bühlmann is Professor of Mathematics and Professor at the Universitat Politècnica de Catalunya. He received the Kurt Statistics, and Director of Foundations of Data Science at ETH Zürich. He Friedrichs Prize, New York University, 1995, and is a Fellow of the American studied mathematics at ETH Zürich and received his doctoral degree in 1993 Mathematical Society, inaugural class of 2012. -
The BEST WRITING on MATHEMATICS
The BEST WRITING on MATHEMATICS 2012 The BEST WRITING on MATHEMATICS 2012 Mircea Pitici, Editor FOREWORD BY DAVID MUMFORD P RI NC E TO N U N IVER S I T Y P RE SS P RI NC E TO N A N D OX FORD Copyright © 2013 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved ISBN 978- 0- 691-15655-2 This book has been composed in Perpetua Printed on acid- free paper. ∞ Printed in the United States of America 1 3 5 7 9 10 8 6 4 2 For my parents Contents Foreword: The Synergy of Pure and Applied Mathematics, of the Abstract and the Concrete DAVID MUMFORD ix Introduction MIRCEA PITICI xvii Why Math Works MARIO LIVIO 1 Is Mathematics Discovered or Invented? TIMOTHY GOWERS 8 The Unplanned Impact of Mathematics PETER ROWLETT 21 An Adventure in the Nth Dimension BRIAN HAYES 30 Structure and Randomness in the Prime Numbers TERENCE TAO 43 The Strangest Numbers in String Theory JOHN C. BAEZ AND JOHN HUERTA 50 Mathematics Meets Photography: The Viewable Sphere DAVID SWART AND BRUCE TORRENCE 61 Dancing Mathematics and the Mathematics of Dance SARAH- MARIE BELCASTRO AND KARL SCHAFFER 79 Can One Hear the Sound of a Theorem? ROB SCHNEIDERMAN 93 Flat- Unfoldability and Woven Origami Tessellations ROBERT J. LANG 113 A Continuous Path from High School Calculus to University Analysis TIMOTHY GOWERS 129 viii Contents Mathematics Teachers’ Subtle, Complex Disciplinary Knowledge BRENT DAVIS 135 How to Be a Good Teacher Is an Undecidable Problem ERICA FLAPAN 141 How Your Philosophy of Mathematics Impacts Your Teaching BONNIE GOLD 149 Variables in Mathematics Education SUSANNA S. -
2017 Magdalen College Record
Magdalen College Record Magdalen College Record 2017 2017 Conference Facilities at Magdalen¢ We are delighted that many members come back to Magdalen for their wedding (exclusive to members), celebration dinner or to hold a conference. We play host to associations and organizations as well as commercial conferences, whilst also accommodating summer schools. The Grove Auditorium seats 160 and has full (HD) projection fa- cilities, and events are supported by our audio-visual technician. We also cater for a similar number in Hall for meals and special banquets. The New Room is available throughout the year for private dining for The cover photograph a minimum of 20, and maximum of 44. was taken by Marcin Sliwa Catherine Hughes or Penny Johnson would be pleased to discuss your requirements, available dates and charges. Please contact the Conference and Accommodation Office at [email protected] Further information is also available at www.magd.ox.ac.uk/conferences For general enquiries on Alumni Events, please contact the Devel- opment Office at [email protected] Magdalen College Record 2017 he Magdalen College Record is published annually, and is circu- Tlated to all members of the College, past and present. If your contact details have changed, please let us know either by writ- ing to the Development Office, Magdalen College, Oxford, OX1 4AU, or by emailing [email protected] General correspondence concerning the Record should be sent to the Editor, Magdalen College Record, Magdalen College, Ox- ford, OX1 4AU, or, preferably, by email to [email protected]. -
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Volume 47 • Issue 1 IMS Bulletin January/February 2018 National Academy new member The US National Academy of Medicine (NAM) has announced the election of 70 reg- CONTENTS ular members and 10 international members. Among them is Nicholas Patrick Jewell, 1 National Academy of University of California, Berkeley. Medicine elects Jewell Election to the Academy is considered one of the highest honors in the fields of 2 Members’ news: Nick Horton, health and medicine, recognizing individuals who have made major contributions to Eric Kolaczyk, Hongzhe Li, the advancement of the medical sciences, health care, and public health. A diversity Runze Li, Douglas Simpson, of talent among NAM’s membership is Greg Lawler, Mike Jordan, Mir assured by its Articles of Organization, Masoom Ali which stipulate that at least one-quarter 3 Journal news: EJP, ECP, Prob of the membership is selected from fields Surveys; OECD guidelines outside the health professions, for exam- 4 Takis Konstantopoulos: new ple, from law, engineering, social sciences, column and the humanities—and statistics. The newly elected members bring 6 Recent papers: Electronic Journal of Probability; Electronic NAM’s total membership to 2,127 and Communications in Probability the number of international members to 172. 11 Special Invited Lecturers; IMS Fellow Nicholas P. Jewell is New Textbook Professor of Biostatistics and Statistics 12 Obituary: Ron Getoor at the University of California, Berkeley. 13 IMS Awards Since arriving at Berkeley in 1981, he has held various academic and administrative 15 Student Puzzle Corner 19; New Researcher Award positions, most notably serving as Vice Provost from 1994 to 2000. -
A Widely Applicable Bayesian Information Criterion
JournalofMachineLearningResearch14(2013)867-897 Submitted 8/12; Revised 2/13; Published 3/13 A Widely Applicable Bayesian Information Criterion Sumio Watanabe [email protected] Department of Computational Intelligence and Systems Science Tokyo Institute of Technology Mailbox G5-19, 4259 Nagatsuta, Midori-ku Yokohama, Japan 226-8502 Editor: Manfred Opper Abstract A statistical model or a learning machine is called regular if the map taking a parameter to a prob- ability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In regular statistical models, the Bayes free energy, which is defined by the minus logarithm of Bayes marginal likelihood, can be asymptotically approximated by the Schwarz Bayes information criterion (BIC), whereas in singular models such approximation does not hold. Recently, it was proved that the Bayes free energy of a singular model is asymptotically given by a generalized formula using a birational invariant, the real log canonical threshold (RLCT), instead of half the number of parameters in BIC. Theoretical values of RLCTs in several statistical models are now being discovered based on algebraic geometrical methodology. However, it has been difficult to estimate the Bayes free energy using only training samples, because an RLCT depends on an unknown true distribution. In the present paper, we define a widely applicable Bayesian information criterion (WBIC) by the average log likelihood function over the posterior distribution with the inverse temperature 1/logn, where n is the number of training samples. We mathematically prove that WBIC has the same asymptotic expansion as the Bayes free energy, even if a statistical model is singular for or unrealizable by a statistical model. -
NEWSLETTER No
NEWSLETTER No. 464 December 2016 ATHENA PRIZE The London Mathematical Society Women in Diversity Conference on 31 October 2016. The Mathematics Committee was presented with medal was presented by Dr Julie Maxton, the inaugural Royal Society Athena Prize (see Executive Director, Royal Society. See page 3 for November LMS Newsletter) at the Royal Society images of the medal. Dr Julie Maxton, Executive Director, Royal Society; Professor John Greenlees, LMS Vice President; Dr Cathy Hobbs; Professor Gwyneth Stallard; Dr Eugenie Hunsicker, Chair, Women in Mathematics Committee SOCIETY MEETINGS AND EVENTS • 16–17 December: Prospects in Mathematics • 5 May 2017: Mary Cartwright Lecture, London Meeting, York page 16 • 1 June 2017: Northern Regional Meeting, York • 20 December: SW & South Wales Regional • 30 June 2017: Graduate Student Meeting, Bath page 15 Meeting, London • 18–22 April 2017: LMS Invited Lectures, Newcastle page 24 • 30 June 2017: Society Meeting, London NEWSLETTER ONLINE: newsletter.lms.ac.uk @LondMathSoc LMS NEWSLETTER http://newsletter.lms.ac.uk Contents No. 464 December 2016 7 18 Calendar of Events 39 British Combinatorial Conference.........21 British Postgraduate Model LMS Items Theory Conference...............................20 Athena Prize............................................1 2 Young Theorists’ Forum..........................21 Caring Supplementary Grants................5 Cecil King Travel Scholarship News 2017 – call for nominations................25 Chern Medal 2018...................................4 Council Diary............................................6