The Theory of the Mathematician Bayes and the “Bayesian”… probabilities

There are many scientists and businessmen around the world who use statistical models in order to make predictions and “manage” the future. Bayesian inference (Bayes theory), named after the mathematician and nonconformist clergyman Thomas Bayes, is widely used to determine how the degree of belief can be modified about a research hypothesis, based on an initial observation. Quite simply, what is the probability that an event B will occur, given an event A.

Thomas Bayes

But all the versions, no matter how uncertain they seem, may come true as it was unfortunately seen in the case of the British technology tycoon Mike Lynch, whose body was recovered on Thursday 22, August morning, about 24 hours after the sinking of the luxury yacht named “Bayesian” in which he celebrated with friends his acquittal in his much-lauded and long-running dispute with HP in the US. Leeds himself was a proponent of Bayes’ theorem (published in 1763 after his death in 1761), according to which a proper understanding of probability can fundamentally lead to more predictable outcomes.

The evolutionary path

And he wasn’t the only one, as AI researchers, including self-driving car designers, use Bayesian software, Bayesian programs, according to Sharon Bertsch McGrayne, author of The Theory That Would Not Die, recognize spam in e-mail, the same models estimate risks in medical surgery and find millions of applications across the planet.

Bayesian thinking was at the heart of Lynchs’ evolutionary path.

Mike Lynch

After all, it was the subject of his PhD at Cambridge and the basis of Autonomy, the software company he founded in 1996 and sold to Hewlett-Packard (HP) for $11.7 billion in 2011.

The years-long legal battle sparked by the sale of Autonomy is considered one of Silicon Valley’s biggest fraud cases.

The overwhelming preponderance of the probabilities

Accused by HP of using “serious accounting irregularities” to inflate the value of Autonomy, Lynch was taken into custody and extradited to America in handcuffs. Facing 15 counts of fraud and conspiracy, he was placed under house arrest in San Francisco.

The odds were not on his side. Less than 1% of federal cases result in acquittals, while the vast majority of defendants plead guilty in exchange for lighter sentences. In fact, Charles Breyer, the judge in the case, had already jailed Sushovan Hussain, Autonomy’s former CFO.

However, Lynch emerged victorious despite the odds being overwhelmingly against him and was cleared of all charges last June.

But some time later the odds “turned” against him. It should be said that Probability Theory first appeared as a theoretical background to uncertainty. The turn to statistics in recent decades shows that the primary interpretation of probability as a measure of the degree of belief that an event will occur is missing. And reality proves it. The tragic irony is that within a Bayesian approach the very event of the accident leads us to fix the probability of such an event occurring (for more analysis please read the analysis titled “The “strange” shipwreck in Sicily: Mike Lynch’s close ties to US and UK intelligence and Darktrace“).

In any case, the distance that separates classical statistics from probabilities lies in the difference between random and uncertain, as the former characterizes the mode of occurrence also related to frequency, while the latter to knowledge or even worse to the lack of it . After all, the “Bayesian” analysis always gives the possibility of realistic upgrading of the information, something that was proved in the most tragic way in the sinking of “Bayesian”.

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