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Post by Arlon10 on Jul 6, 2017 16:08:11 GMT
... Statistic class, first year. Wrong classroom. The practice of statistics is about finding the measurement in a population from measurement of less than the entire population. It is finding a "probability" of sorts, but from direct measurement of more or less real data more or less accurately. Probabilities class, which you have here, is about finding a probability from other probabilities. A problem with finding probabilities from other probabilities is that it requires assumptions not usually found in statistics. Real world events are usually neither totally dependent nor totally independent, without which you have assumed too much. I noticed my opponents assume too much rather often. A statistics class concerns itself with how did you get those probabilities that you started with and whether the measure was conducted properly. You have countenanced no such question. Perhaps you should.
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Post by Eva Yojimbo on Jul 6, 2017 18:48:03 GMT
I think Kiera and AJ are right. If in doubt and the problem is simple enough, a quick Monte Carlo sim can shed some light, as in the following Python code: ... calc probability = 0.666988 I suppose that is the "correct" answer according to Baye's Theorem. I don't see the use of it though. I don't see any realistic scenario where you can benefit from such information. How did anyone know that tech would not outperform the economy without some new idea how the economy would perform? If you have some idea how the economy will perform shouldn't that be factored in? I'm sorry I would not encourage the use of that theorem. One use it does seem to have is showing how bad some guesses can be. 1. It's "Bayes'" or "Bayes's" Theorem, not "Baye's." It was developed by the Reverend Thomas Bayes. 2. The "use" of it is in teaching the correct way to update prior beliefs based on new evidence. As I said in my above post, all correct processing of evidence works via Bayes' Theorem. Yes, as you've mentioned, the results will only be as good and accurate as the data you gather and numbers you use, but as both myself and Kiera said: there's no other/better alternative, and being able to make an educated guess while knowing the right theorem is better than nothing at all. The same principle applies to deductive logic: logic itself can't tell you what propositions are correct, it can only tell you how to correctly (and incorrectly) reason from them to new conclusions. We don't dismiss logic because it doesn't in itself tell us what propositions are correct, and we don't dismiss Bayes because it doesn't in itself tell us when our numbers are accurate. There are also plenty of real-world applications. A classic example that's often given to doctors is this: 1% of women have breast cancer. A new test is will give a positive 90% of the time if the woman has breast cancer, and 10% of the time if the woman doesn't. A woman has a positive test. What's the probability she has breast cancer? Most doctors vastly overestimate this. Bayes' Theorem shows how to process the evidence of the positive test correctly. An actual historical example of Bayes being useful is in how it helped cracked the Enigma code. There was even a book written about it: www.amazon.com/Theory-That-Would-Not-Die/dp/0300188226/
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Post by general313 on Jul 6, 2017 20:31:23 GMT
I suppose that is the "correct" answer according to Baye's Theorem. I don't see the use of it though. I don't see any realistic scenario where you can benefit from such information. How did anyone know that tech would not outperform the economy without some new idea how the economy would perform? If you have some idea how the economy will perform shouldn't that be factored in? I'm sorry I would not encourage the use of that theorem. One use it does seem to have is showing how bad some guesses can be. 1. It's "Bayes'" or "Bayes's" Theorem, not "Baye's." It was developed by the Reverend Thomas Bayes. 2. The "use" of it is in teaching the correct way to update prior beliefs based on new evidence. As I said in my above post, all correct processing of evidence works via Bayes' Theorem. Yes, as you've mentioned, the results will only be as good and accurate as the data you gather and numbers you use, but as both myself and Kiera said: there's no other/better alternative, and being able to make an educated guess while knowing the right theorem is better than nothing at all. The same principle applies to deductive logic: logic itself can't tell you what propositions are correct, it can only tell you how to correctly (and incorrectly) reason from them to new conclusions. We don't dismiss logic because it doesn't in itself tell us what propositions are correct, and we don't dismiss Bayes because it doesn't in itself tell us when our numbers are accurate. There are also plenty of real-world applications. A classic example that's often given to doctors is this: 1% of women have breast cancer. A new test is will give a positive 90% of the time if the woman has breast cancer, and 10% of the time if the woman doesn't. A woman has a positive test. What's the probability she has breast cancer? Most doctors vastly overestimate this. Bayes' Theorem shows how to process the evidence of the positive test correctly. An actual historical example of Bayes being useful is in how it helped cracked the Enigma code. There was even a book written about it: www.amazon.com/Theory-That-Would-Not-Die/dp/0300188226/Very informative, thanks for posting that. I took classes in probability theory and statistical physics in college, but don't recall ever coming across Bayes' Theorem. Have you read the book that you linked to, and if so how would you rate it? It sounds interesting but I'm a little concerned if this reviewer comment is accurate. Thoughts?
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Post by Aj_June on Jul 6, 2017 20:50:21 GMT
1. It's "Bayes'" or "Bayes's" Theorem, not "Baye's." It was developed by the Reverend Thomas Bayes. 2. The "use" of it is in teaching the correct way to update prior beliefs based on new evidence. As I said in my above post, all correct processing of evidence works via Bayes' Theorem. Yes, as you've mentioned, the results will only be as good and accurate as the data you gather and numbers you use, but as both myself and Kiera said: there's no other/better alternative, and being able to make an educated guess while knowing the right theorem is better than nothing at all. The same principle applies to deductive logic: logic itself can't tell you what propositions are correct, it can only tell you how to correctly (and incorrectly) reason from them to new conclusions. We don't dismiss logic because it doesn't in itself tell us what propositions are correct, and we don't dismiss Bayes because it doesn't in itself tell us when our numbers are accurate. There are also plenty of real-world applications. A classic example that's often given to doctors is this: 1% of women have breast cancer. A new test is will give a positive 90% of the time if the woman has breast cancer, and 10% of the time if the woman doesn't. A woman has a positive test. What's the probability she has breast cancer? Most doctors vastly overestimate this. Bayes' Theorem shows how to process the evidence of the positive test correctly. An actual historical example of Bayes being useful is in how it helped cracked the Enigma code. There was even a book written about it: www.amazon.com/Theory-That-Would-Not-Die/dp/0300188226/Very informative, thanks for posting that. I took classes in probability theory and statistical physics in college, but don't recall ever coming across Bayes' Theorem. Have you read the book that you linked to, and if so how would you rate it? It sounds interesting but I'm a little concerned f this reviewer comment is accurate. Thoughts? As mentioned by Eva, in the long term, any prediction based on Bayes' will have a good rate of success with quality empirical data. Edit: In your statistics class you might have read something on total probability theory. Very close to Bayes'
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Post by Eva Yojimbo on Jul 6, 2017 20:51:29 GMT
1. It's "Bayes'" or "Bayes's" Theorem, not "Baye's." It was developed by the Reverend Thomas Bayes. 2. The "use" of it is in teaching the correct way to update prior beliefs based on new evidence. As I said in my above post, all correct processing of evidence works via Bayes' Theorem. Yes, as you've mentioned, the results will only be as good and accurate as the data you gather and numbers you use, but as both myself and Kiera said: there's no other/better alternative, and being able to make an educated guess while knowing the right theorem is better than nothing at all. The same principle applies to deductive logic: logic itself can't tell you what propositions are correct, it can only tell you how to correctly (and incorrectly) reason from them to new conclusions. We don't dismiss logic because it doesn't in itself tell us what propositions are correct, and we don't dismiss Bayes because it doesn't in itself tell us when our numbers are accurate. There are also plenty of real-world applications. A classic example that's often given to doctors is this: 1% of women have breast cancer. A new test is will give a positive 90% of the time if the woman has breast cancer, and 10% of the time if the woman doesn't. A woman has a positive test. What's the probability she has breast cancer? Most doctors vastly overestimate this. Bayes' Theorem shows how to process the evidence of the positive test correctly. An actual historical example of Bayes being useful is in how it helped cracked the Enigma code. There was even a book written about it: www.amazon.com/Theory-That-Would-Not-Die/dp/0300188226/Very informative, thanks for posting that. I took classes in probability theory and statistical physics in college, but don't recall ever coming across Bayes' Theorem. Have you read the book that you linked to, and if so how would you rate it? It sounds interesting but I'm a little concerned if this reviewer comment is accurate. Thoughts? I haven't read that book but I did remember hearing about how Bayes' was used to help crack the Enigma code. From what I gather it tackles the issue mostly from a pop-historical perspective. The one I was recommended (that I also haven't read yet) that delves into Bayes in a more in-depth, textbook-like way is ET Jaynes's Probability Theory: The Logic of Science If you've already studied probability and statistics at a collegiate level then you'd probably get more out of the latter (my not having studied them formally is one thing that's scared me away from that book a bit; my interest in Bayes is more philosophical and my usage pretty idiosyncratic).
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Post by Arlon10 on Jul 6, 2017 22:09:14 GMT
I suppose that is the "correct" answer according to Baye's Theorem. I don't see the use of it though. I don't see any realistic scenario where you can benefit from such information. How did anyone know that tech would not outperform the economy without some new idea how the economy would perform? If you have some idea how the economy will perform shouldn't that be factored in? I'm sorry I would not encourage the use of that theorem. One use it does seem to have is showing how bad some guesses can be. 1. It's "Bayes'" or "Bayes's" Theorem, not "Baye's." It was developed by the Reverend Thomas Bayes. 2. The "use" of it is in teaching the correct way to update prior beliefs based on new evidence. As I said in my above post, all correct processing of evidence works via Bayes' Theorem. Yes, as you've mentioned, the results will only be as good and accurate as the data you gather and numbers you use, but as both myself and Kiera said: there's no other/better alternative, and being able to make an educated guess while knowing the right theorem is better than nothing at all. The same principle applies to deductive logic: logic itself can't tell you what propositions are correct, it can only tell you how to correctly (and incorrectly) reason from them to new conclusions. We don't dismiss logic because it doesn't in itself tell us what propositions are correct, and we don't dismiss Bayes because it doesn't in itself tell us when our numbers are accurate. There are also plenty of real-world applications. A classic example that's often given to doctors is this: 1% of women have breast cancer. A new test is will give a positive 90% of the time if the woman has breast cancer, and 10% of the time if the woman doesn't. A woman has a positive test. What's the probability she has breast cancer? Most doctors vastly overestimate this. Bayes' Theorem shows how to process the evidence of the positive test correctly. An actual historical example of Bayes being useful is in how it helped cracked the Enigma code. There was even a book written about it: www.amazon.com/Theory-That-Would-Not-Die/dp/0300188226/ Okay then, "Bayes' " I have to call foul on the way the problem in this thread was originally worded. "Given the new information that the technology sector will not outperform the market," is wrong. Please observe some correct wording. When considering a large number of years without exception the economy expands in 6 cases out of 10. (That the probability the economy will expand is 60 percent this year is problematic as you will see, but not entirely inaccurate.) When considering a large number of years with exception, that is collecting only those in which the economy does expand, the tech sector outperforms in 7 out of 10 of those cases. When considering a large number of years with exception, that is collecting only those in which the economy does not expand, the tech sector outperforms in 1 out of 10 of those cases. Up to this point is the "old" information. There will be no "new" information. Notice the important correct phrasing ... When considering a large number of years with exception, that is collecting only those (plural!!) in which the tech sector did (past tense) not outperform, in how many of those does the economy not expand?
Now no one will try to solve using "new" information that the tech sector has succeeded. That wasn't "new" information at all anyway. Saying so is entirely incorrect. You were merely being asked to select a different set of the "old" information, those cases (plural!!) where the tech sector did not outperform. In the original wording it appears you actually learned something "new" and now "know" that this year the tech sector will not outperform. You in fact do not. If you word the question properly you will get fewer wrong answers. The expression "new information" in the original wording is bad English and at fault, but that's just one mistake. Another mistake seeing you have not learned anything is that there is no worth to your computation. It's nothing but another way of looking at data you already had. The value of the old information "this" year is nothing much since there is nothing special about this year. Only if you had actual new information could you learn anything. As I already noted elsewhere it is that information rather than the old that you should use to make any further predictions. To the subject of breast cancer, you have supplied no statistical analysis at all, none. You haven't told where you got any of those probabilities. Yet you expect us to gleefully assume we can find other probabilities based on those. We don't find probabilities based on other probabilities in statistics. Real life events are neither totally dependent nor totally independent. We find probabilities based on data collection. When errors appear we correct the method of data collection.
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Post by Eva Yojimbo on Jul 6, 2017 22:44:50 GMT
1. It's "Bayes'" or "Bayes's" Theorem, not "Baye's." It was developed by the Reverend Thomas Bayes. 2. The "use" of it is in teaching the correct way to update prior beliefs based on new evidence. As I said in my above post, all correct processing of evidence works via Bayes' Theorem. Yes, as you've mentioned, the results will only be as good and accurate as the data you gather and numbers you use, but as both myself and Kiera said: there's no other/better alternative, and being able to make an educated guess while knowing the right theorem is better than nothing at all. The same principle applies to deductive logic: logic itself can't tell you what propositions are correct, it can only tell you how to correctly (and incorrectly) reason from them to new conclusions. We don't dismiss logic because it doesn't in itself tell us what propositions are correct, and we don't dismiss Bayes because it doesn't in itself tell us when our numbers are accurate. There are also plenty of real-world applications. A classic example that's often given to doctors is this: 1% of women have breast cancer. A new test is will give a positive 90% of the time if the woman has breast cancer, and 10% of the time if the woman doesn't. A woman has a positive test. What's the probability she has breast cancer? Most doctors vastly overestimate this. Bayes' Theorem shows how to process the evidence of the positive test correctly. An actual historical example of Bayes being useful is in how it helped cracked the Enigma code. There was even a book written about it: www.amazon.com/Theory-That-Would-Not-Die/dp/0300188226/ If you word the question properly you will get fewer wrong answers. If you understood Bayes' Theorem you wouldn't have gotten the answer wrong at all. The wording of the question is tricky, but easily solvable if you know what you're doing. Everyone else in this thread managed to solve it correctly but you, and I managed to solve it correctly back when AJ PMed me about back on the old IMDb and even suggested to him how to solve such problems more quickly. The purpose of Bayes is not to supply statistical analysis, it's to update prior probabilities based on new evidence in the form of conditional probabilities. You apparently didn't grasp the fundamental point I made about the connection with deductive logic. Neither Bayes nor logic can assure that our numbers/propositions are right, and this is neither a flaw nor limitation of either. The assigning of probabilities and determining of true propositions are a completely different area of philosophy, science, and research. If you take the breast cancer example, it is entirely possible to know via statistics the number of women who have breast cancer, and if the results of that test have been researched then it is also possible to know how often it gives true positives VS false positives. It's only by taking those three probabilities together that you can figure out the probability that any given positive means breast cancer as opposed to a false positive. If you don't believe Bayes has any practical application, I provided two books--one pop-historical and one in-depth and technical--that argues otherwise. So if you want to contribute anything meaningful you need to go argue with them and win in your inimitable Arlon way. EDIT: Completely forgot that one of the most modern and pragmatic uses of Bayes' is in Spam Filtering. So if your email filters spam, you can thank Bayes' for that.
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Post by Arlon10 on Jul 6, 2017 23:21:31 GMT
If I applied Bayes' Theorem without regard to the wording of the problem I would have gotten the same answer as everyone else who applied Bayes' Theorem without regard to the wording of the problem. There's "tricky" and "plain wrong." The wording of the question was plain wrong. There must not be any "new" information, and that being the case what happens "this" year is not relevant. Bayes' theorem when used correctly merely looks at existing data from a different perspective as I took great trouble to explain to you and you fail to address here. I never paid any attention to that before, why should I start now? What I said. Says you but not Wikipedia, hmmm? I'm sure that happens to you a lot. Whenever there are "false" positives, negatives or anything else it is important to develop awareness of that. Used correctly Bayes' Theorem can help, but accurate data will still depend on improved methods that can reduce such errors. Any method wrong 10 percent of the time is a waste of money. You don't keep juggling those numbers. You cut off the money for that data collection method. If someone can find more dependable methods you hire that person instead. I have no problem with the "pure" math in Bayes' theorem. It works fine in the problem I worded correctly for you. The only use I have ever seen for it though is showing how wrong some guesses can be. I have not seen and you have not shown any such thing.
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Post by Eva Yojimbo on Jul 6, 2017 23:49:21 GMT
If I applied Bayes' Theorem without regard to the wording of the problem I would have gotten the same answer as everyone else who applied Bayes' Theorem without regard to the wording of the problem. Well, duh, if you pay no attention to how the problem is worded then you'll never get the answer right regardless of the method you use. Welcome to grade-school math/word problem solving. There's nothing "wrong" about the wording. All they did is give you the probability of tech outperforming the market as opposed to tech NOT outperforming the market, which is what you really need to know given the new evidence is that tech won't outperform the market. In that case you just reverse the probabilities given (30% instead of 70%, 90% instead of 10%). Given your penchant for getting these problems/questions dead wrong, perhaps you should start paying attention to everyone else if you want to actually get them right and learn something. Wikipedia phrases it in terms of probability theory and statistics, but you can treat all beliefs as prior probabilities and all new evidence as conditional probabilities. There is a larger philosophical use for Bayes as an ideal model for epistemological reasoning and rationality in general. Only with the types that think they can argue with dictionaries and win. Most everyone else (non-Dunning-Kruger victims) don't have a problem. It's entirely possible that that test is the best you can do as far as accuracy. In any case, the probability that you have cancer given a positive test went from 1% to 10%, and if you took the test again and got another positive it would go from 10% to 50%. I don't see how you figure that's a waste of money to gain that kind of knowledge. There will be plenty of situations in life when we can't do anything to test something to anything near 100% certainty. This is typically why it takes so long for doctors to diagnose certain conditions, because no one test is 100% accurate and infallible, but if several different tests concur then it adds up to a high probability of a given condition. en.wikipedia.org/wiki/Naive_Bayes_spam_filtering
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Post by Arlon10 on Jul 7, 2017 0:31:34 GMT
No, they said there was "new" information that tech does not outperform "this year" (and the probability of the economy expanding was given for "this year" only). I pointed out the problem with that. In order for Bayes' Theorem to work there must not be such "new" information. I got the part right at the outset of using 30 percent. You just stepped in it deeply again. Remember what I said about events in real life not being totally dependent nor totally independent? If one person gets two tests those tests are not totally independent. Part of the reason the test fails if it does might have something to do with the person, the location, or both. In such cases another similar result means close to nothing. See "independent" events. Who? There is a limit to the number of times I will repeat myself and we are already there, amigo. Maybe we can take up these arguments next month after you've had time to adjust.
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Post by Eva Yojimbo on Jul 7, 2017 4:15:07 GMT
No, they said there was "new" information that tech does not outperform "this year" (and the probability of the economy expanding was given for "this year" only). I pointed out the problem with that. In order for Bayes' Theorem to work there must not be such "new" information. I got the part right at the outset of using 30 percent. I must've missed where you "pointed out the problem with that." The "new information" is just the evidence, it's not "new" as in there's no statistical basis for it. Edit: Never mind, I just reread your post above. I guess I assumed the green text was you quoting something else and I didn't read it. I'll give it a look over tomorrow and get back with you if I find it worth responding to. Yes, there could be conditions in which a false positive is given and will continue to be given regardless, but I was not making that assumption. If that was the case then other tests would have to be performed to see if they corroborated the first test, but in either case the probability still went from 1% to 10%, and we know that thanks to Bayes. I can't for the life of me figure why you're asking "who" in response to that link. Yes, I need to adjust; not you, the only guy that got the OP problem wrong and started bringing up issues that had nothing to do with Bayes but rather a general problem about gathering accurate data/statistics.
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Post by phludowin on Jul 7, 2017 6:57:39 GMT
Actually, upon further reflection, Arlon10 and Eva Yojimbo are both partly right on this issue. Bayes's theorem is used to calculate probabilities based on the knowledge of other probabilities- But the question here is formulated in an ambiguous way. Like: Did the economist make his 60% growth prediction knowing about the tech sector not outperforming the market? I guess not. And is it a one-way conditionality? Meaning: Does the tech sector outperform the market with 70% probability if the economy expand, or iff the economy expands? Maybe a different (and possibly more schoolbook friendly) way to formulate the problem would have been as follows: "The young uprising country of Bayesiana has a thriving economy. The probability that their economy expands in any given year is 60%. The Bayesianian tech sector is an important factor for their economy, and a good general indicator for the wellbeing of their economy. If the Bayesianian economy expands, their tech sector will outperform the market with a probability of 70%. But if the Bayesianian economy does not expand, their tech sector will outperform the market with a probability of only 10%. Calculate the probability that the Bayesianian economy did not expand in a given year, knowing that in that year, the tech sector did not outperform the market." The answer, as established before, is 2/3.
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Post by Aj_June on Jul 7, 2017 8:19:49 GMT
With all due respect to you, Arlon, you may be a good writer but you are not the best learner. This isn't first instance when you started attacking the question itself. You should just be happy to learn something new but you first attacked the theorem itself and now the wording of the question. I had put an actual retired question of LSAT and you kept calling the question itself as dubious. theoncomingstorm (cash), I and @jwtutor had no problem solving that question. Do you think Law School Admission Council would have released a wrong question? Similarly on this instance, the question was tricky but not wrong. This is how a CFA question is made to fool test takers. It's not difficult but it tries to trick the test takers who have to rush all along because of lack of time (240 questions like that in a day/6 hours).
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Post by general313 on Jul 7, 2017 14:05:35 GMT
70% probability if the economy expand, or iff the economy expands? The original problem stated "The technology sector has a 70%probability of outperforming the market if the economy expands and a 10% probability of outperforming the market if the economy does not expand." That is clear and unambiguous.
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Post by Eva Yojimbo on Jul 7, 2017 19:07:33 GMT
70% probability if the economy expand, or iff the economy expands? The original problem stated "The technology sector has a 70%probability of outperforming the market if the economy expands and a 10% probability of outperforming the market if the economy does not expand." That is clear and unambiguous. "Given" might've been a better term than "if," but I can't imagine that tripping many people up.
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Post by Aj_June on Jul 16, 2017 0:44:40 GMT
The original problem stated "The technology sector has a 70%probability of outperforming the market if the economy expands and a 10% probability of outperforming the market if the economy does not expand." That is clear and unambiguous. "Given" might've been a better term than "if," but I can't imagine that tripping many people up. Eva - jw-Tutor had referred me to approach to you as he said you were a big fan of Bayes' Theorem. Just wanted to ask if you have any info on properties of log-normal distribution? I have had easy time understanding chi square distribution and F distribution but log-normal distribution still gives me some trouble. No problems if you don't as I have some youtube videos but I need to see them.
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Post by Eva Yojimbo on Jul 16, 2017 2:48:56 GMT
"Given" might've been a better term than "if," but I can't imagine that tripping many people up. Just wanted to ask if you have any info on properties of log-normal distribution? I have had easy time understanding chi square distribution and F distribution but log-normal distribution still gives me some trouble. No problems if you don't as I have some youtube videos but I need to see them. Sorry but no; that's completely out of my very limited area of "expertise" (if I dare even call what's in my area "expertise."). Good luck, though!
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Post by Aj_June on Jul 16, 2017 3:49:38 GMT
Just wanted to ask if you have any info on properties of log-normal distribution? I have had easy time understanding chi square distribution and F distribution but log-normal distribution still gives me some trouble. No problems if you don't as I have some youtube videos but I need to see them. Sorry but no; that's completely out of my very limited area of "expertise" (if I dare even call what's in my area "expertise."). Good luck, though! Thanks, Eva. I still have your explanation of how to tackle Bayes' questions effectively. That was very helpful. I will look at some youtube videos for getting a solid grip on log-normal thing. Last year I had developed a gambling system which failed towards the end and gave me an overall loss but I will try to incorporate as many new things as I can in my system this year to refine it.
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Post by tickingmask on Jul 16, 2017 11:06:40 GMT
log-normal distribution still gives me some trouble. Does standard normal distribution give you trouble? All that log-normal distribution is, is standard normal distribution but on a logarithmic scale instead of a linear one. So under a log-normal distribution, the probability of X being less than half the modal value is the same as the probability of X being more than double. If you draw a log-normal distribution on a linear scale, its modal value would be the same, but its distribution would be skewed to the right. Log-normal distributions tend to be used a lot in calculation of derivatives values where it is assumed (fairly dodgily, I might add) that market volatilities cause values of the underlying assets to do a time-based random walk abour a log-normal distribution. This is used as a basis for pricing methods like the Black Scholes model, for example. What else do you need to know?
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Post by Aj_June on Jul 16, 2017 12:10:47 GMT
log-normal distribution still gives me some trouble. Does standard normal distribution give you trouble? All that log-normal distribution is, is standard normal distribution but on a logarithmic scale instead of a linear one. So under a log-normal distribution, the probability of X being less than half the modal value is the same as the probability of X being more than double. If you draw a log-normal distribution on a linear scale, its modal value would be the same, but its distribution would be skewed to the right. Log-normal distributions tend to be used a lot in calculation of derivatives values where it is assumed (fairly dodgily, I might add) that market volatilities cause values of the underlying assets to do a time-based random walk abour a log-normal distribution. This is used as a basis for pricing methods like the Black Scholes model, for example. What else do you need to know? Thanks! I am pretty good with normal distribution. The questions that assume lognormal distribution really confused me initially. For example, they assume that returns are normally distributed but prices are log-normally distributed. The book explained that it is because prices are never negative and bounded by zero from left. After some time I did get the main properties of it. Next they tried to mix the concept of lognormal distribution with continuously compounded rates of return. I am scheduled to read Black Scholes model next month but it is just that I have never felt comfortable with lognoramal distribution. It's something that I have to see from the book again and again and I still manage to get the answers wrong. Thankfully, I haven't got to deal a lot with lognormal distributions like I have to with normal distributions. I think my main problem is inability to identify assumptions of when lognormal distribution is appropriate.
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