Posts Tagged 'Statistics'

An English Lady with a Certain Taste

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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

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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].

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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.

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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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