Bayes’s theorem as a model for learning
Let’s say we did an experiment and got data set
Now, let’s say we did another experiment and got data
Now, we plug in Bayes’s theorem applied to our first data set, giving
By the product rule, the denominator is
Inserting these expressions into equation the above expression for
So, acquiring more data gave us more information about our hypothesis
in that same way as if we just combined
Bayes theorem thus describes how we learn from data. We acquire data, and that updates our posterior distribution. That posterior distribution then becomes the prior distribution for interpreting the next data set we acquire, and so on. Data constantly update our knowledge.