## On the history of mathematical statistics in Lund

During the first decades of the 20th century statistical science became recognized as an academic discipline in its own right. Its role in social and natural sciences and in economics seemed obvious, but the role of mathematics in statistics was much discussed. In May 1915, Lund university named Sven Dag Wicksell the first academic teacher in Mathematical statistics, the first in Sweden and the third in the world.Read the story of how it happened in
Why distinguish between statistics and mathematical statistics -
the case of Swedish academia a study by Peter Guttorp and Georg Lindgren, and take a look at the presentation
Fahlbeck vs. Charlier - Wicksell in the middle - in the early days of Lund statistics.

## New Wafo version, January 2016

The**Wafo**toolbox has been upgraded to work together with Matlab R2014b and later. It can be downloaded, together with a tutorial, from the Wafo homepage. The new version, tentatively called

**Wafo26**includes a module for generation and analysis of Gauss-Lagrange and Stokes-Lagrange waves.

## International textbooks

### Introductory textbook on stationary processes

A new introductory textbook on Stationary stochastic processes for scientists and engineers appeared in October 2013 at Chapman & Hall/CRC, written by myself, Holger Rootzén and Maria Sandsten. It represents "episode one" in companion with the more advanced book from 2012. Click on the book to access solutions to the exercises in the book and Matlab material for practical experience.### Advanced textbook on stationary processes

The advanced textbook on Stationary stochastic processes: Theory and applications appeared in October 2012 at Chapman & Hall/CRC. It is intended for "a second course" on the topic and covers spectral theory, linear filters, ergodicity, random fields, extreme values and sample function properties. Click on the book to get access to an update, with comments and some errata.## Projects

At present (winter 2016) I am involved in the following**major project**:

WAFO,
a MATLAB toolbox for Wave Analysis for Fatigue and Oceanography

**Some recent projects:**

SARMA, a Nordic Network on Statistical
Approaches to Regional Climate Models for Adaptation,
supported by NordForsk through
Toppforskningsinitiativet.

Event in Lund: Workshop on Statistical approaches
to down- and upscaling in climate models, April 27-29, 2011.

Vind i Öresund, INTERREG IVA project for regional integration in Öresund together with DTU Informatik. Supported by the European Union,

SEAMOCS, a EU FP6 Marie Curie Research Training Network for stochastics in the marin sciences.

FRIVA, Framework Programme for Risk and Vulnerability Analysis

A list of **other old projects**.

## Research interests

Stochastic processes and their applications in engineering, statistics and the environment, stochastic models in marine science, stochastic wave models, Markov regime models. Statistics in ophthalmology. Statistics education.

## Publications

### Publications available in LU database

### Full list of publications

### Recent publications

- Lindgren, G.:
Horseshoe-like patterns in first-order 3D random Gauss-Lagrange waves with directional spreading.
*Waves in Random and Complex Media*, (2015); DOI: 10.1080/17455030.2015.10822673. - Lindgren, G.: Asymmetric waves in wave energy systems analysed by the stochastic Gauss-Lagrange wave model.
*Proceedings of the Estonian Academy of Sciences*; Vol 64 (2015) 291-296. - Lindgren, G.: A detailed statistical representation of the local structure of optical vortices in random wavefields.
*Journal of Optics A: Pure and Applied Optics*, 14 (2012) 035704. doi:10.1088/2040-8978/14/3/035704. - Lindgren, G. and Lindgren, F.: Stochastic asymmetry properties of 3D Gauss-Lagrange ocean waves with directional spreading.
*Stochastic Models*, 23:3 (2011) 490-520; DOI: 10.1080/15326349.2011.593410 . - Lindgren, G., Bolin, D. and Lindgren, F.:
Non-traditional stochastic models for ocean waves -
Lagrange models and nested SPDE models.
*Eur. Phys. J. Special Topics*, 185 (2010) 209-224; DOI: 10.1140/epjst/e2010-01250-y. - Lindgren, G.: Slope distribution in front-back asymmetric stochastic Lagrange time waves.
*Advances in Applied Probability*, 42 (2010) 489-508. - Grage, H., Holst, J., Lindgren, G. and Saklak, M.: Level crossing prediction with neural networks.
*Methodol Comput Appl Probab*, (2009) DOI: 10/1007/s11009-009-9153-3. - Lindgren, G.: Exact asymmetric slope distributions in stochastic
Gauss-Lagrange ocean waves.
*Applied Ocean Research*, 31 (2009) 65-73. - Lindgren, G. and Åberg, S.: First order stochastic Lagrange models for front-back
asymmetric ocean waves.
*J. Offshore Mech. Arct. Eng.*131 (2009) 031602-1 - 031602-8. - Guttorp, P. and Lindgren, G.: Karl Pearson and the Scandinavian School of Statistics.
*International Statistical Review*, 77 (2009) 64-71. - Aberg, S. and Lindgren, G.: Height distributions of
stochastic Lagrange ocean waves.
*Probabilistic Engineering Mechanics*, Vol 23 (2008) 359-363. - Lindgren, G.: Slepian models for the stochastic shape of individual
Lagrange sea waves.
*Advances in Applied Probability*, Vol 38 (2006) 430-450. - Lindgren, G. and Zetterqvist, L.: Teaching modern engineering statistics: the contribution of collaboration and shared views of the roles of mathematical statistics in engineering. Invited paper to ICOTS-7, Salvador, Brazil 2006.
- Lindgren, G. & Broberg, K.B.: Cycle range distributions
for Gaussian processes - exact and approximate results.
*Extremes*, 7 (2004) 69 - 89. - Brodtkorb, P.A., Johannesson, P., Lindgren, G., Rychlik, I,
Rydén, J. & Sjö, E.: WAFO - a Matlab toolbox for analysis
of random waves and loads.
*ISOPE'2000*. - Lindgren, G.: Wave analysis by Slepian models.
*Probabilistic Engineering Mechanics*, 15 (2000) 49-57.

### Some old publications, which are still much cited

*Extremes and crossings:*

Two early papers, Some properties of a Gaussian process near a local maximum, in the Annals of Mathematical Statistics, (1970), and Local maxima of Gaussian fields, Arkiv för Matematik (1972), are now often quoted, and they form the basis for much of my later research on statistical extremes and their applications.

*Markov regime models and switching autoregression:*

The paper Markov regime models for mixed distributions and switching regressions, Scandinavian Journal of Statistics (1978), is based on a technical report, 1976 from Umeå university. The report includes two examples, Ex 2.3 and 3.1, of a Markov Switching Autoregression, later studied by i.a. Hamilton.

## Presentations

- 2015: Stochastic models for ocean waves - Gaussian fields made more realistic by Rice formula and some physics. Talk in Statistics seminar, University of Bath, November 24, 2015.
- 2015: Fahlbeck vs. Charlier - Wicksell in the middle - in the early days of Lund statistics. Talk at Mathematical statistics Centenary 2015, May 12.
- 2014: Asymmetric waves in wave energy systems analysed by the Gauss-Lagrange wave model. Talk at IUTAM Symposium 2014 on Complexity of Nonlinear waves, Tallin, Estonia, September 8-12, 2014.
- 2013: Extremes, wave asymmetry, and other stochastic properties of an ocean wave energy system - aspects on model choice in an engineering application. Talk at EVT2013, Extremes in Vimeiro today, Vimeiro, Portugal, September 8 - 11, 2013.
- 2013: (Extremes and related properties of) Stochastic asymmetric Lagrange waves. Talk at Symposium on recent advances in Extreme value theory, honoring Ross Leadbetter, Lisbon, March 18 - 20, 2013.
- 2012: Extremvärdesteori som ett hjälpmedel att sätta gränser - Blickar bakåt och framåt. Talk at Cramérsällskapets årsmöte i Alnarp, 22 mars 2012 (in Swedish).
- 2011: Stochastic properties of optical black holes. Statistics seminar, Lund September 9, 2011, and UNC October 24, 2011.
- 2011: Statistical/Mathematical wave models - for what purpose? Discussion in session IPS098 at ISI2011, Dublin, August 24, 2011.
- 2011: Random deformation of Gaussian fields with an applications to Lagrange models for asymmetric ocean waves. Talk at ISI2011, Dublin, August 23, 2011.
- 2011: Random load models for use in stochastic fatigue life assessment - some unpredicted consequences of Bertram Broberg's urge to understand. Talk at the 3rd Bertram Broberg symposium, Lund, May 30, 2011.
- 2011: Stochastic 3D Lagrange waves, asymmetry properties and consequences for marine safety. Talk at European Geosciences Union General Assembly 2011, Wien, April 8, 2011.
- 2010: 3D stochastic Lagrange model for asymmetric ocean waves. Stochastic field Workshop, Lund, November 17, 2010.
- 2010: Extremes for data with phase shifting seasons - some observations from marine climate. Talk at Workshop on Extreme events in climate and weather", Banff, August 22-27, 2010.
- 2010: Ulf Grenander - "mathematical tools for practical problems". Invited talk at 23rd Nordic Conference on Mathematical Statistics, Voss, June 15, 2010.
- 2010: Fatigue limit for Rice's formula = + infinity. Talk at the Jacques de Maré symposium in Göteborg, June 4, 2010.
- 2009: Realistic and practical stochastic models for ocean waves. Invited talk at XI CLAPEM, Naiguatá, Venezuela, November 1-6, 2009.
- 2009: Further development of the stochastic Lagrange model for asymmetric ocean waves - some new results. Talk at Seamocs meeting, Toulouse, Sept8-10, 2009.
- 2009: Lagrange models for asymmetric random waves. Poster at Seamocs meeting at Preluna Hotel and Spa, Malta, March 16-20, 2009.
- 2008: Stochastic models in marine sciences. Invited talk at International Workshop on Applied Probability, Compiègne, July 10, 2008.

## Teaching - old

- SMHI-kurs
- Stationary stochastic processes, PhD course, fall 2006 and spring 2007 (also 2000, 2002, spring/fall 2004)

### Mailing address:

Georg LindgrenMathematical Statistics

Centre for Mathematical Sciences

Box 118, SE-221 00 Lund, Sweden

### Phones & email addresses:

+46 46 22 285 47 (office)+46 46 22 285 50 (dept)

+46 46 22 246 23 (fax)

e-mail: georg (at) maths.lth.se

### Visitors address:

MH:238Mathematics building

Sölvegatan 18

Lund, Sweden

Last modified: June 5, 2014
by Georg Lindgren

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