(This post is not an attempt to convey anything new, but is instead an attempt to convey the concept of Bayesian reasoning as simply as possible. There have been other elementary posts that have covered how to use Bayes’ theorem: here, here, here and here)

Bayes’ theorem is about the probability that something is true given some piece or pieces of evidence. In a really simple form it is basically the equation below:

This will be explained using the following coin flipping scenario:

If someone is flipping two coins: one fair and one biased (has heads on both sides), then what is the probability that the coin flipped was the fair coin given that you know that the result of the coin being flipped was heads?

Let’s figure this out by listing out the potential states using a decision tree:

We know that the tail state is not true because the result of the coin being flipped was heads. So, let’s update the decision tree:

The decision tree now lists all of the possible states given that the result was heads.

Let's now plug in the values into the formula. We know that there are three potential states. One in which the coin is fair and two in which it is biased. Let's assume that each state has the same likelihood.

So, the result is: 1 / 1 + 2 which is 1 / 3 which equals 33%.Using the formula we have found out that there is 33% chance that the coin flipped was the fair one when we already know that the result of the flip was heads.

At this point you you may be thinking what any of this has to do with bayesian reasoning. Well, the relation is that the above formula is pretty much the same as Bayes’ theorem which in its explicit form is:

You can see that P(B|A) * P(A) (in bold) is on both the top and the bottom of the equation. It represents “expected number of times it’s true” in the generic formula above. P(B|~A) * P(~A) represents "expected number of times it's false".

You don’t need to worry about what the whole formula means yet as this post is just about how to use Bayesian reasoning and why it is useful. If you want to find out how to deduce Bayes' theorem, check out this post. If you want some examples of how to use Bayes' theorem see one of these posts: 1, 2, 3 and 4.

Let’s now continue on. This time

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LifeofLaughter

LifeofLaughter

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