mathematics

Niels Keiding

Niels Keiding is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Niels Keiding rather than just read about it. In short: Niels Keiding (14 May 1944 – 3 March 2022) was a Danish biostatistician. Biography Education Keiding studied at the University of Copenhagen, graduating with a cand.stat. degree (roughly equivalent to a Master's degree in other countries) under supervisor Anders Hald in 1968.

Key takeaways

Niels Keiding belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Niels Keiding to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Niels Keiding from memory before moving on to harder problems.

Reference excerpt

Niels Keiding (14 May 1944 – 3 March 2022) was a Danish biostatistician.

Biography

Education Keiding studied at the University of Copenhagen, graduating with a cand.stat. degree (roughly equivalent to a Master's degree in other countries) under supervisor Anders Hald in 1968.

Teaching and professional experience At the University of Copenhagen, Keiding successively held assistant, associate and, from 1984, full professor positions, the latter in the section of Biostatistics within the Faculty of Health Sciences. In 1971 he was one of the founders of the Danish Society of Theoretical Statistics (DSTS), serving as its secretary from 1971–1975. The Scandinavian Journal of Statistics was founded in 1974, with DSTS being one of its four societal board members. He was head of the Biostatistics section until three years prior to retirement. In 2014 he became Professor emeritus at the section.

Research and development Keiding's research spanned several fields. In demography, he published on nonparametric inference for the Lexis diagram. With coauthors he contributed to event history analysis, including to models where only partial information is available. He applied the latter to time-to-pregnancy (TTP), which is the timespan from the start of when a couple tries to become pregnant until they succeed. In a survey with coauthors, he clarified how survival analysis is used to analyze TTP. His book, Statistical models based on counting processes, written jointly with Per Kragh Andersen, Ørnulf Borgan, and Richard D. Gill, has been cited extensively in the medical literature and been lauded for its "lucid" exposition of theoretical and practical aspects. Its survey of statistical models based on counting processes has been called "thorough". Keiding co-authored an influential meta-analysis, known as Carlsen study after the name of the first author, that showed a significant decline in human sperm count and volume from 1938 to 1990. He also wrote about the history of the use of martingales in survival analysis (with coauthors), and of demography, in particular age-period-cohort analysis in the 19th century.

Work for international scientific organisations Keiding served as treasurer of the Bernoulli Society for Mathematical Statistics and Probability (1981–1987), chairman of the board of the Scandinavian Journal of Statistics (1988–1991), and president (1992–1993) of the Biometric Society. He was a member of the Research Section Committee of the Royal Statistical Society (1999–2003), and member of council and several ad hoc committees in the Institute of Mathematical Statistics (IMS) and the International Statistical Institute (ISI). He was president-elect of the ISI in 2003–2005, and president in 2005–2007.

Selected works

Books Kragh Andersen, Per; Borgan, Ørnulf; Gill, Richard D; Keiding, Niels (2012). Statistical models based on counting processes. Springer Science & Business Media. ISBN 978-1-4612-4348-9.

Articles E Carlsen, A Giwercman, N Keiding, NE Skakkebæk, Evidence for decreasing quality of semen during past 50 years. British Medical Journal 305 (6854), 609-613 (1992) J Toppari, JC Larsen, P Christiansen, A Giwercman, P Grandjean, et al., Male reproductive health and environmental xenoestrogens. Environmental Health Perspectives 104 (suppl 4), 741-803 (1996) WHO Expert Committee on Leprosy: Seventh Report. WHO Expert Committee on Leprosy, World Health Organization (1998) PK Andersen, N Keiding, Multi-state models for event history analysis. Statistical Methods in Medical Research 11 (2), 91-115 (2002)

Honours and awards His honours and awards include:

References

External links ISI members' news, In Memoriam: Niels Keiding 2022-03-14.

Illustrations

Worked examples

Example 1 — a first encounter with Niels Keiding

Start with the simplest possible case. Write down what Niels Keiding claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Niels Keiding before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Niels Keiding ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Niels Keiding

In research: Niels Keiding appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Niels Keiding in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Niels Keiding is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1944 births, 2022 deaths, Academic staff of the University of Copenhagen, so understanding it makes those chapters shorter.
In everyday life: Look for Niels Keiding outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Niels Keiding in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Niels Keiding means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Niels Keiding out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Niels Keiding in simple terms?

Niels Keiding (14 May 1944 – 3 March 2022) was a Danish biostatistician. Biography Education Keiding studied at the University of Copenhagen, graduating with a cand.stat. degree (roughly equivalent to a Master's degree in other countries) under supervisor Anders Hald in 1968.

Why does Niels Keiding matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Niels Keiding?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Niels Keiding.