Posts Tagged 'Statistics'

How many numbers begin with a 1? More than 30%!

The irregular distribution of the first digits of numbers in data-bases provides a valuable tool for fraud detection. A remarkable rule that applies to many datasets was accidentally discovered by an American physicist, Frank Benford, who described his discovery in a 1938 paper, “The Law of Anomalous Numbers” [TM181 or search for “thatsmaths” at irishtimes.com].

Benford-Distribution-3

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An English Lady with a Certain Taste

Ronald-Fisher-1913

Ronald Fisher in 1913

One hundred years ago, an English lady, Dr Muriel Bristol, amazed some leading statisticians by proving that she could determine by taste the order in which the constituents are poured in a cup of tea. One of the statisticians was Ronald Fisher. The other was William Roach, who was to marry Dr Bristol shortly afterwards.

Many decisions in medicine, economics and other fields depend on carefully designed experiments. For example, before a new treatment is proposed, its efficacy must be established by a series of rigorous tests. Everyone is different, and no one course of treatment is necessarily best in all cases. Statistical evaluation of data is an essential part of the evaluation of new drugs [TM170 or search for “thatsmaths” at irishtimes.com].

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ToplDice is Markovian

Many problems in probability are solved by assuming independence of separate experiments. When we toss a coin, it is assumed that the outcome does not depend on the results of previous tosses. Similarly, each cast of a die is assumed to be independent of previous casts.

However, this assumption is frequently invalid. Draw a card from a shuffled deck and reveal it. Then place it on the bottom and draw another card. The odds have changed: if the first card was an ace, the chances that the second is also an ace have diminished.

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Andrey Markov’s Brilliant Ideas are still a Driving Force

AA-Markov-SMALL

A A Markov (1856-1922)

Imagine examining the first 20,000 letters of a book, counting frequencies and studying patterns. This is precisely what Andrey Markov did when he analyzed the text of Alexander Pushkin’s verse novel Eugene Onegin. This work comprises almost 400 stanzas of iambic tetrameter and is a classic of Russian literature. Markov studied the way vowels and consonants alternate and deduced the probabilities of a vowel being followed by a another vowel, by a consonant, and so on. He was applying a statistical model that he had developed in 1906 and that we now call a Markov Process or Markov chain. [TM123 or search for “thatsmaths” at irishtimes.com].

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The Improbability Principle

Extremely improbable events are commonplace.

It’s an unusual day if nothing unusual happens”. This aphorism encapsulates a characteristic pattern of events called the Improbability Principle. Popularised by statistician Sir David Hand, emeritus professor at Imperial College London, it codifies the paradoxical idea that extremely improbable events happen frequently.  [TM112 or search for “thatsmaths” at irishtimes.com].

Improbability-Principle-Top

From front cover of  The Improbability Principle

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The Citizens’ Assembly: Why do 10 Counties have no Members?

Recently, the Irish Government established the Citizens’ Assembly, a body of 99 citizens that will consider a number of constitutional issues. The Assembly meets on Saturday to continue its deliberations on the Eighth Amendment to the Constitution, which concerns the ban on abortion. It will report to the Oireachtas (Parliament) on this issue in June [TM106 or search for “thatsmaths” at irishtimes.com].

citizensassembly-logo

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Twenty Heads in Succession: How Long will we Wait?

If three flips of a coin produce three heads, there is no surprise. But if 20 successive heads show up, you should be suspicious: the chances of this are less than one in a a million, so it is more likely than not that the coin is unbalanced.

euro-frontback-ie

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Mathematics Solving Crimes

What use is maths? Why should we learn it? A forensic scientist could answer FornsicMaths-CraigAdamthat virtually all the mathematics we learn at school is used to solve crimes. Forensic science considers physical evidence relating to criminal activity and practitioners need competence in mathematics as well as in the physical, chemical and biological sciences [TM080: search for “thatsmaths” at irishtimes.com ].

Trigonometry, the measurement of triangles, is used in the analysis of blood spatter. The shape indicates the direction from which the blood has come. The most probable scenario resulting in blood spatter on walls and floor can be reconstructed using trigonometric analysis. Such analysis can also determine whether the blood originated from a single source or from multiple sources.

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The Faraday of Statistics

This week, That’s Maths in The Irish Times ( TM044 ) is about the originator of Students t-distribution.

In October 2012 a plaque was unveiled at St Patrick’s National School, Blackrock, to commemorate William Sealy Gosset, who had lived nearby for 22 years. Sir Ronald Fisher, a giant among statisticians, called Gosset “The Faraday of Statistics”, recognising his ability to grasp general principles and apply them to problems of practical significance.

Plaque at St Patrick's National School, Hollypark, Blackrock, where William Gosset lived from 1913 to 1935.

Plaque at St Patrick’s National School, Hollypark, Blackrock, where William Gosset lived from 1913 to 1935.

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Population Projections

The Population Division of the United Nations marked 31 October 2011 as the “Day of Seven Billion”. While that was a publicity gambit, world population is now above this figure and climbing. The global ecosystem is seriously stressed, and climate change is greatly aggravated by the expanding population. Accurate estimates of growth are essential for assessing our future well-being. This week, That’s Maths in The Irish Times ( TM034  ) is about population growth over this century. Continue reading ‘Population Projections’

A Simple Growth Function

Three Styles of Growth

Early models of population growth represented the number of people as an exponential function of time,

\displaystyle N(t) = N_0 \exp(t/\tau)

where {\tau} is the e-folding time. For every period of length {\tau}, the population increases by a factor {e\approx 2.7}. Exponential growth was assumed by Thomas Malthus (1798), and he predicted that the population would exhaust the food supply within a half-century. Continue reading ‘A Simple Growth Function’

Bayes Rules OK

This week, That’s Maths ( TM018 ) deals with the “war” between Bayesians and frequentists, a long-running conflict that has now subsided. It is 250 years since the presentation of Bayes’ results to the Royal Society in 1763.

The column below was inspired by a book, The Theory that would not Die, by Sharon Bertsch McGrayne, published by Yale University Press in 2011.
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