Name: The power of Bayesian reasoning | BBC Ideas
Uploaded: 2026-01-22T18:17:32.000Z
Duration: 4 min 56 s
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Adverbs of manner

every time you change your mind based on new information, like rethinking a decision after hearing a friend's advice, you're using something called Bayesian reasoning.

Basic passive voice

Bayesian reasoning was first articulated by the Reverend Thomas Bayes, a clergyman from Tunbridge Wells in southern England, way back in the 18th century.

In fact, his theory wasn't published until two years after he had died.

But his work has gone on to profoundly shape science, medicine, and artificial intelligence.

It even helped crack the Nazis Enigma code during World War II.

So what is Bayesian reasoning, and how can it help us understand the world?

First, that our beliefs can be expressed as probabilities, and

second, how our beliefs should be revised when we obtain more information.

Essentially, he produced a theory for learning from experience.

Bayesian analysis can be used in any situation where each new item of information changes our beliefs.

Alan Turing and his team at Bletchley park used Bayesian ideas to learn about the settings of Enigma machines in World War II, changing their opinion as new patterns were found.

The spam filter on your email account will use Bayesian analysis to change its probability that your email message is spam as each new suspicious feature is detected.

Take breast cancer Screening in the UK, mammograms are rather accurate, detecting about 90% of cancers, and

97% of women without cancer correctly get a negative test result.

Let's consider what we would expect to happen to 100 women being tested.

Based on past experience of the rate of breast cancer among women getting mammograms, we would expect one out of the hundred to have cancer, and

that case is almost certain to be picked up on the mammogram.

Of the remaining 99 without cancer, we would expect three women to get a false positive result.

So in total, we expect one plus three equals four positive tests.

From this perspective, looking only at the women who get a positive result, perhaps the test does not seem so accurate.

Around three out of four or 75% of the women recalled don't have cancer.

Further tests should rapidly identify these three false positives.

This is an example of using Bayesian analysis.

Since we are taking into account the base rate for the condition, our prior probability that a random woman being tested has breast cancer is 1%.

And after getting a positive test result, this is updated to what is called a posterior probability, which is 1 out of 4 or 25% of course, further investigations will eventually change the probabilities of those who are recalled either to 0% or less, fortunately 100%.

The use of Bayesian analysis in medical testing is now standard.

However, more controversial is the use of Bayesian methods in science, so called Bayesian inference.

The traditional view of science is that it is a completely objective activity, that data is analyzed without preconceptions and the results speak for the the Bayesian perspective is somewhat different.

It acknowledges that there are always judgments underlying every analysis and that we don't start from a blank slate.

Each set of data adds to our existing knowledge rather than standing entirely on its own.

For example, clinical trials of new drugs are not designed in complete ignorance.

There is always some historical evidence available about the potential effectiveness of the new therapy, and

expert judgments can be elicited and used to prioritize investigations and produce efficient designs.

And it's even thought that we have Bayesian brains.

We don't start from scratch to interpret our sensations for each second that passes.

Instead, we always have prior expectations of what we might experience next, and

then new observations update our beliefs accordingly.

Fundamentally, Bayesian ideas reflect what it means to be human.

we always have prior expectations of what might happen next, and

we revise that uncertainty as we learn from experience, all based on the ideas of a rather obscure 18th century cleric from Tunbridge Wells.

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The power of Bayesian reasoning | BBC Ideas

perspective

articulate

vital

prioritize