Let me get this straight please. Let us suppose that I am looking at one company only, which happens to be in MAESTRO's universe, something that I am not aware off. It can also be in NOBODY's universe and in FACELESS' universe. Should I worry about their statistics? Let's be serious. This only makes sense when you are trading a portofolio. It has no effect on individual securities. How can subjective probabilities affect anything, anyway?
Can you relate to an example below and then extrapolate it to my example? It may help. 1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer? What would be your answer?
Reading some of the replies here I realized that there are a few conclusions that I can easily draw: 1. A vast majority of population has incredible troubles with the notion of Randomness. Most of people have very strong preconceived notions with regards this phenomenon and have preconditioned their brains to be BIASed towards determinism. People in general do not understand what the Randomness actually means and how to exploit it in their day-to-day activities. A very few people have actually EXPERIENCED the distribution curves including the normal one. A very few even looked at "Galton's Bean Machine" and have no idea of its significance. 2. Even among mathematicians (and I had this experience many times) there is absolutely no understanding of the Bayes's Theorem, its practicality, its usefulness for the decision making process in highly uncertain environments. Even people who TEACH probabilities and statistics have trouble comprehending and using this theorem. 3. Games that we play all day long as we live our lives could be dramatically enhanced by self education in the area of modern probabilities theory. The knowledge obtained by that education could be easily implemented in trading (Decision Making of Buying and Selling, Money and Risk Management, Portfolio management etc.) 4. We have no trouble accepting the statistical odds in a game of poker, but we have difficulties to believe that the markets are simply a large poker game on its own. Even if I can make a slightest difference in this situation I would consider my efforts well worth the time I spent typing my posts. So, I will continue to try making people curios about the subject. Once again, please read this material. http://yudkowsky.net/rational/bayes Cheers, MAESTRO
Well... Let me give it a try... Hopefully I set it up right...! P(A given B) = .80*.01/.80*.1+.096*.99 P(A given B) = .008/.008+.09504 P(A given B) = .008/.10304 P(A given B) = .0776 OR 7.76% The probability that a woman given a mammography actually has breast cancer is 7.76 %.
PERFECT!!!! Can you also see the similarity of this example with the one I posted earlier? And, in general, with the situations that we experience in the markets every day? Thank you for your help! You participation is very important! The conclusion that we draw from this example is that intuitively the probability should be very high, but in reality it is very low. It makes designing a trading strategy that banks on the majority of traders being wrong in their assumptions very possible! Just think of it. Isn't it an edge (and very reliable one too!). If you make a bet whether the probability of the example above is less than 10% majority of people would take that bet and lose! Cheers, MAESTRO
Thank you... I'm looking at the example that you provided but I'm finding it difficult to set up the problem... We're looking at... if at .80 then .90 chance of making high if not, .70 chance of retracing If at .10 of the the daily high, what is the chance of making a high? So this would mean that you're at .90 of the daily range...??? 1-.1=.90... This is confusing me... Anyway, this is how I set it up... P(A given B) = .80*.90 / .80*.90+.70*.90 P(A given B) = .72/.72 + .63 P(A given B) = .72/1.35 P(A given B) = .53 OR 53 % Meaning that you have a 53 % chance of reaching a new high if at 10 % of the high...
Man, you are good! So, if we only have 53% of reaching the high if you are that close to it can't you not think of the algo that exploits it and makes a bet with others that believe in fact that it is close to 90% chance? I am sure you can! So, here is a very simple proof of Bayes's usefulness! Thank you again! Very refreshing! Cheers, MAESTRO
MAESTRO, I believe you and happy that you continue. Too late, probably, but here are the bits I didn't include in my previous posts. When most of the day's range is covered or after a very big gap, it feels like, most of the time, that it's done with the move and can reverse at any moment. Yes, it may go much futher, so don't go against it. They teach us that it will, most likely, go much futher than you can imagine but again, it feels like it's too late to jump in. Secondly. Very often, while researching a strategy, I go nuts when I come across the word "sometimes". How am I supposed to trade the "sometimes"?? Yours, MAESTRO, is "a second opinion" I've been waiting for a long time and will follow you closely despite the fact I understand very little of what you are talking about. Thank you.
All of this discussion has been incredibly eye-opening. Absolutely fascinating stuff, with diverse applications! Deeply appreciate your desire to provoke these insights.