Frequentist or Bayesian?

Which are you when it comes to probability and
statistics, a Bayesian or a Frequentist? Here a
simple way of explaining the difference.


"The Bayesian is asked to make bets, which may include anything from which fly will crawl up a wall faster, to which prisoners should go to jail. He has a big box with a crank. He knows that if he puts absolutely everything he knows into the box, including his personal opinion, and turns the handle, it will make the best possible decision for him.

The frequentist is asked to write reports. He has a big black book of rules. If the situation he is asked to make a report on is covered by his rulebook, he can follow the rules and write a report so carefully worded that it is wrong, at worst, one time in 100."

Bayesian's are called optimists, Frequentist's are called
pessimists. Most gambling statiticians are Frequentist's,
they believe totally in the long term results. Bayesian's
are more optimistic, they like to take chances and not
see things as so black and white. Frequentist's tend to
think the Bayesian approach is nonsense, and they can
become quite angry if you even try and discuss it with
them. They know what they know and thats that.

The Bayesian approach dominated statistics for 300 years,
until the Frequentist's took over at the start of the 20th
century. Bayesian's are on the rise again, if we can only
convince the Frequentist's that we didn't all ride the
short blue bus to our 'special' school when were kids.

It is hard to explain in layman's terms what the difference is. I do know that I endured the wrath of a Frequentist when I wrote about the results in the Reid/Angle Senate race. I said something like, "Based on the Associated Press poll, the odds of Reid winning are x%." That is verboten to Frequentists. They would say there was nothing random about the election results, but the poll was the random thing. While that is true, I still don't see what is wrong about making statements like what I did.

Here is a simpler example. Suppose the dealer in pai gow poker shakes the dice but hasn't lifted up the cup yet. What are the odds he rolled a seven? I think this question would make the hair on the back of a Frequentist's neck stand up. He would say the outcome is already determined, so there is nothing random about it any longer. A Bayesian I think would have no problem with saying 1/6.

Quote: Wizard

I do know that I endured the wrath of a Frequentist when I wrote about the results in the Reid/Angle Senate race.

Frequentists view it almost like a religion.
The frequentist view of probability can't
take into account prior information, so it's
quite limited. The frequentist way is to see
probability as a relative frequency; it's just
a ratio of the 'favourable' events to the
total number of equally likely events in
the long term. Bayesian probability is much
more useful for predicting future events based on
prior information, plus you don't need to
have masses of data to calculate the relative
frequency.

Jaynes (1995) is described by Persi Diaconis as a "hard sell" of the Bayesian approach, but it's a good text nonetheless. From the preface:

Quote:

To explain the situation as we see it presently: The traditional frequentist methods which use
only sampling distributions are usable and useful in many particularly simple, idealized problems;
but they represent the most proscribed special cases of probability theory, because they presuppose
conditions (independent repetitions of a random experiment but no relevant prior information)
that are hardly ever met in real problems. This approach is quite inadequate for the current needs
of science.

The book is available free on the 'Net:
Probability Theory: The Logic of Science

Quote: EvenBob

Bayesian's are called optimists, Frequentist's are called pessimists. Most gambling statiticians are Frequentist's, they believe totally in the long term results. Bayesian's are more optimistic, they like to take chances and not see things as so black and white.

I don't think this is actually an accurate representation of the interpretations. It's really about as accurate as saying "Mathematicians are people dealing with pencils and paper, and physicists are people who have to touch everything with their hands."

As such I conclude that stationery store clerks are Frequentist mathematicians and Strauss-Kahn is a Bayesian physicist.

I've worked with probability my entire career, and I have absolutely no idea what you guys are talking about. You lost me right from the beginning when you talked about "placing a bet on which prisoner should go to jail." This phrase is meaningless to me. You can place a bet on which prisoner will go to jail, or you can make a decision about which prisoner should go to jail, but how do you place a bet on which prisoner should go to jail?

I found this quote on the wikipedia page about probability interpretations:

"It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis."

The difference between Bayesian and Frequentist is... terminological (that's really a word?), and I personally think has little bearing on the actual applications of probability and statistics. People who care about this care a little too much about something that just doesn't matter.

Quote: dwheatley

People who care about this care a little too much about something that just doesn't matter.

Thats all well and good, until you actually
have a Frequentist screaming in your face
that you're deluded and insane if you
think Bayesian probability has any merit.
There are some conclusions that can be
arrived at only from a Bayesian approach,
and this makes a lot of Frequentists crazy.

Other than on the internet between people who are really neither frequentist nor bayesian, but rather not statisticians at all, where and when does that actually happen?

Quote: Wizard

Here is a simpler example. Suppose the dealer in pai gow poker shakes the dice but hasn't lifted up the cup yet. What are the odds he rolled a seven? I think this question would make the hair on the back of a Frequentist's neck stand up. He would say the outcome is already determined, so there is nothing random about it any longer. A Bayesian I think would have no problem with saying 1/6.

The Bayesian must not know that there are 3 dice in the cup and the odds that he rolled a 7 are 15 in 216.