I do think Bayes is an improvement over the frequentist methods. But I do think that it’s not the main place where people go wrong.
The main failure I see is the “What a coincidence!” failure. People notice an event that is a one in a billion chance. They say to themselves “Wow ! There was only one chance in a billion for that to happen by chance. This means there must be something special about me/the universe/a higher power/whatever.”
They completely neglect two other numbers.
The number of events that occur every day. You get 86400 seconds every day, and the proportion of those when you’re awake is a time when something unlikely could occur.
The number of other possible unlikely events that you would also have noticed. This is a pretty big number in its own right.
Once you’ve taken these into account, you discover that you actually ought to expect to experience a steady flow of apparently coincidental unlikely events throughout your life. It would be notable if it didn’t happen.
I suspect this is the most important step for most people—the principle of thinking numerically about the things that happen in an orderly way. Going on from there to Bayes’ theorem is then a matter of being taught how to do the maths correctly.
I do think Bayes is an improvement over the frequentist methods. But I do think that it’s not the main place where people go wrong.
The main failure I see is the “What a coincidence!” failure. People notice an event that is a one in a billion chance. They say to themselves “Wow ! There was only one chance in a billion for that to happen by chance. This means there must be something special about me/the universe/a higher power/whatever.”
They completely neglect two other numbers.
The number of events that occur every day. You get 86400 seconds every day, and the proportion of those when you’re awake is a time when something unlikely could occur.
The number of other possible unlikely events that you would also have noticed. This is a pretty big number in its own right.
Once you’ve taken these into account, you discover that you actually ought to expect to experience a steady flow of apparently coincidental unlikely events throughout your life. It would be notable if it didn’t happen.
I suspect this is the most important step for most people—the principle of thinking numerically about the things that happen in an orderly way. Going on from there to Bayes’ theorem is then a matter of being taught how to do the maths correctly.