Bayesian point of view

Supose we are about to bet in car racing.
I'm an expert mechanic and could identify a car defect very quickly.
There are 12 cars to compete in this 1-week-racing.
I analize and determine that 3 of the 12 cars have more probability to win the race.
The other 9 cars will not stand the 5000-lap-race close to the leading car.
My prior is that these 3 cars have more P than 3/12 to win. The P-value could be determine by my expertise skill. I stated that these 3 cars have 5% advantage to win over the other 9.
So, my 3 cars has the P 3,165/12 to win.
Questions:
1)As we make this prior before any car lap it could be no accurate. How do we know the accurate strength of this prior?
2)As races are all day long we have the change to gauge our predictions. Supose we see the first 1200 laps where our 3 favorites cars won 330 of them. How much data do we need to certify our prior? What if they win 300 320 or 400 of the 1200?
3)What are the diferencies with a frequentist how starts analizing data without a subjective prior?

Best regards
Ybot

Require more data. What is the shoe size of each driver ?

Now you know why the Good Reverend Bayes didn't have his theorem published until after he had kicked the bucket.

It is a hard realm to catch for regular gambler.
I'd be glad to read any of your comments to clarify Reverend's thoughs
Warm regards

Bayes' Theorem has been outlawed in the UK. And rightfully so!

Quote: Buzzard

Bayes' Theorem has been outlawed in the UK. And rightfully so!

Huh??

Switch was called as an expert witness and was responsible for this ruling.

http://www.theguardian.com/law/2011/oct/02/formula-justice-bayes-theorem-miscarriage

What about all the "bayesianism"?

Hey, ask Switch. He was the expert witness the judge relied upon.

Quote: ybot

Supose we are about to bet in car racing.
I'm an expert mechanic and could identify a car defect very quickly.
There are 12 cars to compete in this 1-week-racing.
I analize and determine that 3 of the 12 cars have more probability to win the race.
The other 9 cars will not stand the 5000-lap-race close to the leading car.
My prior is that these 3 cars have more P than 3/12 to win. The P-value could be determine by my expertise skill. I stated that these 3 cars have 5% advantage to win over the other 9.
So, my 3 cars has the P 3,165/12 to win.
Questions:
1)As we make this prior before any car lap it could be no accurate. How do we know the accurate strength of this prior?
2)As races are all day long we have the change to gauge our predictions. Supose we see the first 1200 laps where our 3 favorites cars won 330 of them. How much data do we need to certify our prior? What if they win 300 320 or 400 of the 1200?
3)What are the diferencies with a frequentist how starts analizing data without a subjective prior?

Best regards
Ybot

You would have to have access to the cars themselves... engines, suspension, drag, etc, for your expert analysis to be valid for most of the cars. Sure there are always a few in any sport that have almost no chance to win, but most sports are also very competitive at the top and the difference between winning and losing is so small that it's on field (or track) decisions that make the difference.


ZCore13

ZCORE13, we are suposed to know that these 3 car have the advantage.

1. What do you call "accurate strehgth"?
2. What do you call "certify" the prior?
3. A frequentist is not trying to asses a prior, so what exactly are you willing to compare?

Kubikulann,
1. the way to take a prior is subjective, so there must be a way to gauge the likelyhood of the prior
2. A doublecheck, a confirmation
3. I'm trying to use bayesian rules to spend the less time in tests

1. Two schools of thought, here. The first says, "This is subjective, you do not have likelihood". The second tries to give reasons for that particular prior.
Actually, if there are reasons, it is not a prior anymore, it is already posterior to *some* information.
Which leads to
2. You will never "confirm" your prior. Bayes formula is here to incorporate new info in order to transform your prior into a posterior. That posterior will dfinitely be different from your prior (or else, the information was useless).

Some people have tried to put a "confidence index" on priors, but that is just a funny way of building more complicated prior structures. The philosophy behind is not changed.

3. What tests? Testing is frequentist.

Kubikulann, I apologize for my ignorance.
I just wanted to undestand how a bayesian sees probability to accelarate the undestanding of an event.
There must be many situations where bayesian win.
I ask for your kind advise to enlighten my mind.
Thank you very much

Quote: ybot

Kubikulann, I apologize for my ignorance.
I just wanted to undestand how a bayesian sees probability to accelarate the undestanding of an event.

A priori, you ignore the value of a parameter that describe the probability of the event.
What you do is make educated guesses about the possible values: that is your prior (subjective) probability density.

Then, you gather observations. These are more in accordance with some values of the parameter, less so with others. Hence, you will adapt your subjective proabbility density to give more weight to the values that are more compatible with observation.
Bayes' formula indicates how to do this adaptation.
The resulting probability density is called the posterior (or conditional). It is partly subjective (the source, your prior) and partly objective (the data).

It is better than the prior, in the sense that it represents the situation more accurately AND allows better predictions. but neither of these is measurable, because the data that could provide a measure are precisely the data that have been used for the adaptation.

Quote: ybot

There must be many situations where bayesian win.

Alas, not! You cannot change the expected value. The only thing you do is better your estimated probabilities, hence your strategy.

I believe, Bayesian probability is the one seen backwards.
It calculates the probability of an event to be dependent or independent.

Going back to the first example, we could calculate the chance one of the car win the race if a racing world champion is the driver.