Probability and Statistics Part 12

Probability and Statistics 12

By Madison Nef

The Difference Between Bayesian and Frequentist Probability

While many times in probability for math we use frequentist probability, there is a second type of probability that we use more often everyday when expressing our opinions and making statements. It is important that these two different probabilities don’t get confused, because they are different in dramatic ways.

Frequentist Probability

Frequentist probability is used more in math and calculations: problems with factual answers. For example, when calculating the probability of getting a 4 when you roll a 6 sided die- we say that we expect to get at least one 4 if we roll the die 6 times. This gives us a probability of 1/6. It is called frequentist probability because we are measuring the frequency of the die rolls and the answers.

Bayesian Probability

Bayesian Probability, on the other hand, is used more when we are talking between each other. We use it to estimate and to express our opinions on what we think a certain probability is- Bayesian probability is more an established guess, nothing else and is usually not very accurate.

To put this method into perspective, a good example is Shakespeare. If you were to ask people “Who wrote Hamlet”, most would say Shakespeare. However, there are rumors that Shakespeare may NOT have written Hamlet. So depending on what you believe, how you would answer that question could differ. Suppose you answer something like “Oh, there is a 98% chance that Shakespeare wrote the Hamlet… but you can’t discount the other 2%”. This is a good example of Bayesian probability at work because it displays your opinion on a certain topic without being exact. We are making a STATEMENT about our belief, which is far different from a frequentist statement.

The way it is different from a frequentist statement is how we arrive at our conclusion. When asked the ‘Hamlet’ question, we wouldn’t arrive at our answer by saying:

“Well, if there were 100 Shakespeares, 98 of them would have written the Hamlet… therefore, there is a 98% chance that the Hamlet was written by Shakespeare!”

That’s a silly way to do things. What works for calculating the probability of drawing a certain card or rolling a certain number doesn’t necessarily work in real-life situations such as the ‘Hamlet’ scenario. No, when we come to a conclusion like that we are more often estimating and guessing… maybe basing it off of something we have read or heard somewhere.

Those are the differences between frequentist and Bayesian probability, and why they are so important… they shouldn’t be confused, because if they are confused, it can be bad. However, I think you’d have to be extremely stupid to mix the two up as they vary so much from each other.

Maddie