Breaking Down Bayesian

Science is the river of life.
And as each droplet of knowledge is added to the flow, it advances slightly, modifying what was previously known.

The 1740’s saw Thomas Bayes, an English reverend, conduct a thought experiment that would impress any modern day psychic. With no more than an assistant, two balls and a table, designed so that a ball thrown at random had an equal chance of landing anywhere on the table, Bayes was to predict where the ball had been thrown without even looking.

Thomas Bayes

Brushing all spirits aside, he began to formulate a theorem which would go on to become paramount in genetic risk assessment and association studies. Bayes relied on gaining new information so that he could narrow down the area in which the ball was likely to be, this was done using a second ball and being told whether it had landed to the left or the right of the original ball. Throw after throw saw the area become smaller and smaller, leading Bayes to discover that: Initial Belief + New Data -> Improved Belief

Nevertheless, the element of guess work did not sit well with our eighteenth century academics, resulting in Bayes never publishing his work. It wasn’t until after his death that Richard Price providentially stumbled upon the discovery whilst going through his friends notes. Price re-edited and shared the findings in ‘the Essay towards Solving a Problem in the Doctrine of Chances’.

With the world bearing a number of exceptional minds, it seems almost inevitable that a theory will be independently rediscovered and Bayesian’s statistical methods are no exception. In 1774, an outstanding mathematician by the name of Pierre Simon Laplace published the mechanism, before awareness of Bayes work. It was only a matter of time before Laplace was enlightened with the initial discovery; this only encouraged him further to develop the theorem, using a huge database – birth records.

Laplace noted that slightly less males than females were being born and having set out a system of inductive reasoning based on probability, he found this to be a recurring trend whilst analysing records from Paris, Naples, St. Petersbury, London, rural France, Egypterica. He went on to state that the trend was ‘a general law for the human race’ and made the Bayes theorem into the mathematical equation that we are familiar with today:

P(C|E) = P(E|C) Pprior(C)
ƩP(E|C`) Pprior(C`)

Calculating the probability of a particular hypothesis, such as the chances of giving birth to a child who is either a carrier or affected by a certain genetic disorder uses Bayes humble equation, as additional information about the pedigree or genetic testing have been shown to vastly improve the results of genetic risk assessment. Single–SNP tests in genome wide association studies demonstrate Bayesian methods advantageous nature when it comes to assessment of association between genetic variant or other phenotypes.

Centuries have passed since Bayes first etched down the roots of probability, a once laughed at belief stands today as a solid concept, guiding us towards more informed future.

Image reproduced from en.wikipedia.org

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About Sumaya Anwar

Sumaya Anwar is a student of biological sciences at UCL, with a special interest in genetics. Having previous experience as a broadcast journalist, producer and researcher, she now actively works as a presenter and writer. An outgoing, sociable person, she is always interested in finding out others opinions in the pursuit of seeing an issue from every angle. This is reflected in her writing, with a versatile style that would suit a multitude of different topics. Holding a strong belief that a combination of ambition and hard work make anything possible, Sumaya perseveres to make science assessable as well as understandable to everyone.
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