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Post by bracknellboy on Aug 1, 2024 15:34:42 GMT
I get it when the priors are obvious / calculable, I struggle more when it's my... opinion... that decides the priors. The author of this particular blog shares your cynicism and struggle: Bayes’ Theorem and Bullshit
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registerme
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Post by registerme on Aug 1, 2024 15:41:57 GMT
I get it when the priors are obvious / calculable, I struggle more when it's my... opinion... that decides the priors. The author of this particular blog shares your cynicism and struggle: Bayes’ Theorem and BullshitThat was an interesting read, thank you for linking it.
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Post by Ace on Aug 1, 2024 15:51:55 GMT
I remember one example a very good mathematician once used to try to explain all this to me. Something to do with a US game show where you have to choose a prize behind a door, and how to maximise your chances of winning eg the car. And how the correct second go was... non-intuitive. Not sure I understand it to this day  . That one's fairly easy to explain. There are 3 doors. Behind one of the doors is a prize, e.g. a car. There is nothing behind the other 2 doors. You get to open one door, if the car is behind it you win the car. So, you choose a door. At this point, the host, who knows which is the door with a prize behind it, opens one of the other doors (never the one you chose). He always opens an empty door. He then offers you a choice; keep your original door or swap to the other closed door. To maximise your chances of winning you should always swap. It doubles your chances. It seems unintuitive because it looks like a simple 50/50 choice. But if you think about it... If you stick, you only win the prize if you chose correctly to start with. So 1/3 probability. If you twist, you only lose if you chose correctly to begin with. 1/3 probability of losing, so 2/3 probability of winning. This is because, if you picked the wrong door to start with and swap doors when offered you always win. Since the host knows which door the prize is behind he must open the empty door, so the other door will always be the winner. Thus you have a 2/3 probability of winning if you switch.
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Post by bernythedolt on Aug 1, 2024 15:54:25 GMT
I remember one example a very good mathematician once used to try to explain all this to me. Something to do with a US game show where you have to choose a prize behind a door, and how to maximise your chances of winning eg the car. And how the correct second go was... non-intuitive. Not sure I understand it to this day . That's the really fascinating Monty Hall problem, and you're far from alone in being flummoxed by the paradox. EDIT: Cross posted with Ace
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registerme
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Post by registerme on Aug 1, 2024 15:58:11 GMT
Yeah. Also thanks to jonno who PMed me the same. |
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james100
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Post by james100 on Aug 1, 2024 16:23:31 GMT
I get it when the priors are obvious / calculable, I struggle more when it's my... opinion... that decides the priors. Do you mean your opinion on whether a specified event ('the prior') has occurred, or whether your personal opinion is the actually the prior event?
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registerme
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Post by registerme on Aug 1, 2024 17:08:15 GMT
I get it when the priors are obvious / calculable, I struggle more when it's my... opinion... that decides the priors. Do you mean your opinion on whether a specified event ('the prior') has occurred, or whether your personal opinion is the actually the prior event? I mean my assessment as to the probability of whatever the prior is occurring. EDIT: Sure, I can iterate around it as I gain more knowledge / experience / insight etc but... it's still my assessment of the probability as opposed to an explicit "exterior" probability.
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angrysaveruk
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Post by angrysaveruk on Aug 1, 2024 17:20:43 GMT
Bayes Theorem is about the laws of conditional probability, the probability of something happening given something else has happened. Say you have two dice A and B what is the chance of getting a 6 and then a 6. Well that is just 1/6 * 1/6 = 1/36. Now say they are magic dice and that if you roll a 6 on the first dice then the chance of rolling a 6 on the second becomes 1/3, the chance of getting a 6 and a 6 becomes 1/6 * 1/3 = 1/18. That is an application of Bayes Theorem because a 6 on the second dice is condition on the first. The formula becomes: P(A) * P(B|A) now when the two events are independent like when they are not magic P(B|A) becomes P(B), when they are magic P(B|A) does not equal P(B). Now that is kind of interesting but there is a mathematical law of conditional probability here which has to apply to all conditional probabilities and can be used to derive things that are not so obvious: P(A) * P(A|B) = P(B) * P(B|A) or more famously P(A) = P(B) * P(B|A) / P(A|B) Basically like alot of math it starts with something very obvious and then ends up with something not obvious and is some hidden law of reality like Pythagoras' theorem. This law would even apply to our magic dice or Assetz Capital*. * - although it would be very hard to work out what getting your money back is actually conditional on. This stuff is tricky and lawd knows it's confused me enough times over the years, but I'm afraid you've mixed up some of your As and Bs in the equation highlighted. The simplest starting point is this: the probability of event A given event B is the probability of both events happening divided by the probability of event B happening. Thanks for pointing that out I had forgotten how this notation worked since I had not looked at this for a number of years. in my equation I thought P(A|B) meant the probability of B occurring given A had occurred, when it means probability of A occurring given B has occurred. I remember thinking about Bayes Theorem a few years ago and thought that P(A) * P(B|A) = P(B) * P(A|B) was the easiest way to think about it. It simply states the obvious that there are two ways to calculate the probability of A and B both occurring together - you can start with the probability of A and then multiply it by the probability of B occurring given A has occurred, or you can start with the probability of B occurring and then multiply it by the probability of A occurring given B has occurred. These have to equal each other by definition. The main use is you can calculate any one of these 4 probabilities from the other 3, which has a number of uses in practice.
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Post by bracknellboy on Aug 1, 2024 17:37:39 GMT
I remember one example a very good mathematician once used to try to explain all this to me. Something to do with a US game show where you have to choose a prize behind a door, and how to maximise your chances of winning eg the car. And how the correct second go was... non-intuitive. Not sure I understand it to this day . That one's fairly easy to explain. There are 3 doors. Behind one of the doors is a prize, e.g. a car. There is nothing behind the other 2 doors. You get to open one door, if the car is behind it you win the car. So, you choose a door. At this point, the host, who knows which is the door with a prize behind it, opens one of the other doors (never the one you chose). He always opens an empty door. He then offers you a choice; keep your original door or swap to the other closed door. To maximise your chances of winning you should always swap. It doubles your chances. It seems unintuitive because it looks like a simple 50/50 choice. But if you think about it... If you stick, you only win the prize if you chose correctly to start with. So 1/3 probability. If you twist, you only lose if you chose correctly to begin with. 1/3 probability of losing, so 2/3 probability of winning. This is because, if you picked the wrong door to start with and swap doors when offered you always win. Since the host knows which door the prize is behind he must open the empty door, so the other door will always be the winner. Thus you have a 2/3 probability of winning if you switch. even reading it laid out like that, it can still feel counterintuitive. But actually drawing it out with 3 doors makes it very clear.
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Post by bracknellboy on Aug 6, 2024 10:35:18 GMT
Reading in the Economist today, article: "kamala Harris Leads Donald Trump in our nationwide poll tracker"*
"...our tracker has a new methodology, designed to account for the rapidly shifting race. Each poll is an imperfect estimate of the state of play. We use a Bayesian statistical model to simulate...."
Well obviously, of course you do. :-)
*I should note at this point that they are in no way even attempting to predict the actual winner, and the lead they are referring to is as wafer thin as a Mr Creosote after dinner mint. The main thrust of the article is around the impact of the change of candidate.
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keitha
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Post by keitha on Aug 6, 2024 10:50:44 GMT
the probability of any given share increasing in price over a year is A and the probability of it falling is B
in my experience A tends to diminish and B to increase the more time I spend researching that stock and then make a purchase.
next time I'm looking I will add all the ones I put down as possible buys in a watch list and observe over a period.
I also think where company A buys company B out the likelihood of shares in A dropping significantly after the buy out is approaching 1 if I own shares in B
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Post by bracknellboy on Aug 6, 2024 11:03:19 GMT
the probability of any given share increasing in price over a year is A and the probability of it falling is B in my experience A tends to diminish and B to increase the more time I spend researching that stock and then make a purchase. next time I'm looking I will add all the ones I put down as possible buys in a watch list and observe over a period. I also think where company A buys company B out the likelihood of shares in A dropping significantly after the buy out is approaching 1 if I own shares in BI think you'll find that is independent of whether you own it or not. I recall that it is a truism that the best way of destroying shareholder value in a company is for it to acquire or "merge" with another. Of course sometimes it does work, but too often M&As seem to be driven by large but badly run companies looking for a way to overcome their declining/market lagging position, or egos of CEOs/Chairs/Boards, or pressure from shareholders for successful but perhaps slightly boring companies to make use of a cash pile they are sitting on. In the first case, a badly run company doesn't stop being so just because you've injected a new market positioning; in the second case, egos which make leaders think they can run another organisation better than the incumbents can be fatally flawed, especially if it is taking them into new product-market combinations; and the last too often they'd have been better using the cash for internal investment/share buybacks/or hold onto to make them cash rich in the land of paupers come the next economic turn down. In all cases they are likely to be paying a significant premium to current value, a premium which is all too often not justified by subsequent outcomes.
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