We have been oversold on the base rate fallacy in probabilistic judgment from an empirical, normative, and methodological standpoint. A generic information about how frequently an event occurs naturally. medical tests, drug tests, etc. If we test 100,000 people with this test, we get: As a person that receives a positive test result, how confident should you be in trusting that result? 6. From a personal perspective, I am still a little wary as I do not have full faith in my ability to reliably identify such trends in a timely manner due to my inexperience, ignorance and so on. The description of John practically has the word Satanist on the tip of our tongues, and when the question comes, we are all too eager to declare that he is much more likely to be a Satanist than a Christian. The base-rate fallacy only occurs with frequentist methods because they cannot use prior information in a straightforward way. Hope that makes sense. An overwhelming proportion of people are sober, therefore the probability of a false positive (5%) is much more prominent than the 100% probability of a true positive. The so-called Bayes Rule or Bayes Formula is useful when trying to interpret the results of diagnostic tests with known or estimated population-level prevalence, e.g. On the other hand, with Sensitivity at 70% the probability of infection, given a negative test result, is not zero, but depends on the Base Rate. Base rate fallacy/false positive paradox is derived from Bayes theorem. Base Rates and Bayes’ Theorem. Applications and examples. Is it easier? Much of the time it is really difficult to get a read on most of the market. Depletion was increasing. or the base rate fallacy? As we shall see, assessments that underestimate the importance of a statistical base rate commit the fallacy known as ‘base rate neglect’. And if you do discover that ignorance runs a little deeper than you hoped, well, then there's a hedge for that by the name of diversification. Despite John’s appearance increasing the probability that he considers himself a Satanist, the fact is that there are around 2 billion Christians in the world and very few Satanists. Base rate fallacy. It sounds fancy but we actually already use it to reason in our everyday lives. Unfortunately, the human brain does not always deal with evidence properly. I also recommend: Reminisences of a Stockmarket Trader, One up on Wall St and Where are the Customers Yachts, in particular. This finding has been used to argue that intervi… Namely, if the Base rate is low, say 0.1%, the probability is practically zero. kind of stuff which is at base rather unedifying. So even if he had selected his stocks at random from the pool that remained after removing those stocks that did not satisfy his rules, I suspect he would still have done very well over the years (although perhaps not as well as he actually has done after using his skill and judgement in selecting individual stocks from that pool). Base Rate Neglect or Base Rate Fallacy refers to our tendency to ignore data about what usually happens and instead focus just on new, recent, or interesting information. But if the Base Rate is higher, it is well above zero. Lets see how that looks like, by comparing a rare disease (Multiple sclerosis) with a more common disease (lactose intolerance, technically not a disease). - He tries to buy stocks that are on modest valuations, which he defines as stocks that have an attractive yield and a low price earnings ratio and /or a discount to net asset value / real worth. Interesting what you say about picking sectors, it makes sense in the Bayesian context and the house builders you mention are quite a good example. Ian, I've just finished reading the book 'How to make a million - slowly' by Lord John Lee, who has been an extremely successful private investor over many years. One great example of the Bayes theorem and how it impacts our daily decision making is the base rate fallacy. Thomas Bayes and was first published in 1763, 2 years after his death. Koehler: Base rate fallacy superiority of the nonnative rule reduces to an untested empirical claim. Behavioral and brain sciences, 19(1), 1-17. Have a good evening, Bayes Theorem is a mathematical equation where you can input the Base Rate for an event along with the probabilities associated with new information to get the actual overall probability for the event. The base rate fallacy and its impact on decision making was first popularised by Amos Tversky and Daniel Kahneman in the early 1970’s. the proportion of those who have a given condition, is lower than the test’s false positive rate, even tests that have a very low chance of giving a false positive in an individual case will give more false than true positives overall. really summarised the idea concisely and in very simple language - I may have to borrow your phrasing in the future! ( Log Out / - He prefers 'family-run' companies in which the directors have large shareholdings themselves, have 'clean' reputations and have an attitude of being 'stewards' of their shareholders money. Geeky Definition of Base Rate Fallacy: The Base Rate Fallacy is an error in reasoning which occurs when someone reaches a conclusion that fails to account for an earlier premise – usually a base rate, a probability or some other statistic. Base rate fallacy, also called base rate neglect or base rate bias, is a formal fallacy.If presented with related base rate information (i.e. After that, the servant threw other balls on the same table and was ask to tell Bayes, where this (second, third, fourth…) ball has fallen in relationship to the mark of the first ball. We write that the probability of the event is . All the best, A recent opinion piece in the New York Times introduced the idea of the “Base Rate Fallacy.”. generic, general information) and specific information (information only pertaining to a certain case), the mind tends to ignore the former and focus on the latter. I really think you are talking about something quite unrelated to the subject under discussion here. Base rate fallacy. Base rate fallacy, or base rate neglect, is a cognitive error whereby too little weight is placed on the base, or original rate, of possibility (e.g., the probability of A given B). Bayes' theorem for the layman. The chance that somethingin the outcome space occurs is 100%, because the outcome space contains ever… Bayes’2. 1. yes but what on earth does any of that have to do with Bayes Theorem? support the ongoing hypothesis or refute the held beliefs. The Bayesian Doctor will calculate the updated belief based on this information using Bayes Theorem and update the chart of 'Updated Beliefs'. Therefore, in practice we almost always have to expand: Bayesian theorem basically tells us to look at all the cases where the evidence is true and then looking at the proportion of these evidences, where the hypothesis is also true. Suppose you came to the realisation that the oil sector was poised to outperform. [Again, this reduces the chances of fraud by the management at the expense of shareholders.] The evidence would suggest that experts and amateurs alike are poor forecasters whether it comes to company earnings or macro events - it seems the future just isn't all that clear, whatever the scale! The base rate fallacy, also called base rate neglect or base rate bias, is a formal fallacy.If presented with related base rate information (i.e. One great example of the Bayes theorem and how it impacts our daily decision making is the base rate fallacy. If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). - He prefers companies that have had few changes in their directors and few changes in their auditors. The theorem concerns the incorporation of new information into old, in order to accurately determine the revised probability of an event in light of the new information. Let’s suppose that there is a test for telling you if you will develop lactose intolerance in your life. Let P(A) denote the probability of the event A. Answer to the Thought Experiment: The exact answer to this problem depends upon what percentage of the population is homosexual. Consequently there are more Christians who look like satanists than there are satanists who look like satanists" Tom, http://www.aaii.com/stock-screens?a=menubarHome. When I started more serious investing I spent a lot of time reading over 50 books and looking for web based information that would give me an edge over the market. So we are restricting our view to where the evidences holds. In other words, he greatly improved his 'base rate' probabilities of investing success by following those rules...." Change ), You are commenting using your Facebook account. Why would I be more likely to get it right just because I'm analysing a different aspect of the future? Bayesian models are more intuitive to correctly specify than frequentist tests. In short, it describes the tendency of people to focus on case specific information and to ignore broader base rate information when making decisions involving probabilities. I cannot find any of that reflected in your discussion of John Lee's approach that will help others to emulate it. - He looks for moderately optimistic or better chairman's / CEO's most recent comments. 2.1 The base rate fallacy. Not a bad shout to get it as an audio book too - I spend a lot of time reading (too much according to some) and have been looking around for material to listen to while I run etc. I'm not saying I disagree, I'm just curious as to how you (or anyone else?) Therefore I think it makes sense for me to apply Bayesian thinking to an area that I might consider to be a little more timeless. I'm only about half way through but his thinking on the subject is great and has added some clarity to my own ideas about this particular tendency affects the investment process - hence the article! In fact it is the opposite of drunken rationale and takes you though a history of the development of randomness theory and the need for the evolutionary human brain to look for cause and effect patterns that are either not there, or that we misinterpret. Conclusion On the other hand, with Sensitivity at 70% the probability of infection, given a negative test result, is not zero, but depends on the Base Rate. I very recently started Kahneman's book myself (after it sitting in the ever growing 'to read' pile for months) and as you say he covers Bayes' Theorem well. In other words the base rate for share price growth in the oil sector would likely be stronger than the base rate for some other sector - say retail. Easy Definition of Base Rate Fallacy: Don't think "99% accurate" means a 1% failure rate.There's far more to think about before you can work out the failure rate. The scenario looks at a driver being stopped and breathalysed and aims to calculate the probability that a driver who fails the test is actually over the limit. - He uses a 20% stop-loss rule to sell any poorly-performing stocks, but he ignores stop-losses if there is a major overall market fall. General explanation from Wikipedia: When the incidence, i.e. The rules that John Lee uses, according to his book, include the following [I assume he won't mind me summarising them here,as this is likely to increase sales of his book]: Why do knowers of Bayes's Theorem still commit the Base Rate Fallacy? Why would I be more likely to get it right just because I'm analysing a different aspect of the future? In relation to stockpicking I am reminded of the book, "Simple, But Not Easy" - Stockpicking is simple but its not easy to be successful. Base rate fallacy/false positive paradox is derived from Bayes theorem. Conclusion5. This is because I think a large part of John Lee's success was probably due to the rules he used to restrict the pool of stocks from which he constructed his portfolios. In that case, each new ball (new information) updated his belief. Population growth was strong. Ask Question Asked 6 years, 3 months ... ("prevalence" or base rate probability). Thanks, I have been listening to an excellent audiobook in the car (also available as a book) called, "The Drunkard's Walk: How Randomness Rules" by Prof L. Mlodinow . Now you have pointed it out it it seems blindingly obvious! Impact on Intrusion Detection Systems 5. Seems to me that your thought process leads to the idea of emulating investment heroes - "What would Warren Buffett do?" Again I think this must improve the probability of long-term success of the stocks in his portfolio.] the proportion of those who have a given condition, is lower than the test’s false positive rate, even tests that have a very low chance of giving a false positive in an individual case will give more false than … Our prior belief of having the disease is just the distribution of the disease in the population, so 65% or 0.65 (P (Li)). But if the individual company was in a sector that was going downwards then even a strong outperformance of its peers might still deliver a dismal performance in absolute terms. Hi Ian, Especially once you consider that these trends can persist for extended periods of time I suppose it could indeed be easier to identify a sector that is performing well and is likely to continue to do so. 5. In retrospect perhaps I should have opted for plain old clarity instead. If Hand Dare events, then: P(P(HjD) = DjH)P(H) P(D) Our view is that Bayes’ theorem forms the foundation for inferential statistics. PKA - He likes to invest in companies in which a number of directors are buying stocks in their own company using their own savings (as opposed to being granted options). This is where we find out that our minds are poorly primed to deal intuitively with probabilistic reasoning. The English statistician Thomas Bayes has done an interesting experiment on how to visualize that. Another early explanation of the base rate fallacy can be found in Maya Bar-Hillel’s 1980 paper, “The base-rate fallacy in probability judgments”. Tom, I think your article is excellent, but it's use of the mathematical term Bayes Theorem might frighten a lot of people who are not mathematicians. Why do knowers of Bayes's Theorem still commit the Base Rate Fallacy? Thanks - my apologies for the confusion! If so, why? In my opinion just a few successful calls which are used as the basis for significant investments and which are held for significant periods can deliver life changing returns. I am familiar with Bayes theorem and I am a big fan of StockRanks but I hadn't made the connection. In the taxicab example, the base rate for blue cabs was 15% 15 %. Now, lets say, that a similar test as above is developed for this disease, i.e. If we look at the investment process through this probabilistic lens, what can consideration of base rates and Bayes’ theorem offer us? Base Rate Fallacy: This occurs when you estimate P(a|b) to be higher than it really is, because you didn’t take into account the low value (Base Rate) of P(a). The axioms of probability are mathematical rules that probability must satisfy. I think that is the rational response to the Bayesian insights. Jun 8, 2020 epidemiology. Which might also strengthen the case for IT's or OEICs or ETF's which provide broad coverage of target sectors. Consumption was growing strongly. The rate at which something happens in general is called the base rate. The rate at which something happens in general is called the base rate. When the incidence, i.e. Explained based on a test for a rare disease: Basically, when the percentage of people with a disease is lower than the test’s false positive rate, the chance of getting a false positive is higher than actually having the disease. Birn-baum showed that behavior described as "ne-glect of base rate" may be consistent with ra-tional Bayesian utilization of the base rate. A really excellent and thought provoking piece, thank you. To date my second best sector based calls have been in fixed income pref shares, where I arrived late but still in time to join in. Good luck with your investing, We hope that these four examples helped clarify a misinterpretation of Bayes’ rule that is common among newcomers to Bayesian inference: change in belief does not equal posterior belief. But if we do the test with 100,000 people again, we get: Due to the rare occurence of this disease the confidence in the test, even though the test is as good as the one above, goes down to less that 50%, i.e. When we rst learned Bayes’ theorem we worked an example about screening tests showing that P(DjH) can be very di erent from P(HjD). At the empirical level, a thorough examination of the base rate literature (including the famous lawyer–engineer problem) does not support the conventional wisdom that people routinely ignore base rates. As with the base rate fallacy, this process is best outlined with an example, for which I will use example 2 on the same Wikipedia page linked above. The structure of this problem is the same as that of the base rate fallacy. An overwhelming proportion of people are sober, therefore the probability of a false positive (5%) is much more prominent than the 100% probability of a true positive. We can avoid this fallacy using a fundamental law of probability, Bayes’ theorem. Consequently there are more Christians who look like satanists than there are satanists who look like satanists. In fact at the moment I have a stockpicked quality/momentum type portfolio and a more recently a rules based high Stockrank portfolio to see what happens. Christians might possess the same characteristics only rarely but their numbers are big. … Generally, when you see evidence, it can partly confirm your hypothesis, but at the same time also partly confirm another (competing) hypothesis. Base rate fallacy example. [Of course, some start-ups, biotechs and exploration stocks go onto doing extremely well, but the odds of selecting those in advance are small; by excluding such companies I think he improves his probability of out-performing the stock market as a whole.] Example 1 given on the Wikipedia page is clear and easy to picture. [Small companies tend to perform better over the long-run than larger ones, although that is not the case in every year.] Etc etc etc. Yes great article. 2. Where do you stop with this line of thinking though? When evaluating the probability of an event―for instance, diagnosing a disease, there are two types of information that may be available. But it is frequently possible to get a bearing on just one or two sectors - banks, oil companies, house builders and to act accordingly without having to complement that insight by picking the top performing individual stocks. It is remarkable just how many of these US "Guru" screen selections have beaten the US market, without direct human intervention. P(E|H) is the probability of the evidence if the hypothesis is true. If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). [It is well known that 'value' stocks and stocks with high dividend yields tend as a group to out-perform over the long-run.] But, the big but in general, hospitals double check some positive results and you therefore could trust your hospitals. Impact on Intrusion Detection Systems4. When the incidence of a disease in a population is low, unless the test … Let A and B be events. However, to do that, we need to include the possibility that we could be one of the rare false positives. One night, a cab is involved in a hit and run accident. People tend to simply ignore the base rates, hence it is called (base rate neglect). Base Rate Fallacy。 The Base Rate in our case is 0.001 and 0.999 probabilities. Someone else who fancies themselves at stock picking would be sticking individual companies under their microscope and assessing their potential as individuals. is has the same 99.9% true positive rate and the probability of being tested negative, while still developing MS is also pretty low (false positive: 0.02 %). The base rate fallacy and its impact on decision making was first popularised by Amos Tversky and Daniel Kahneman in the early 1970’s. Interesting, thanks for getting back to me. Quite a few of his examples relate to gambling, but they could equally as well be attributed to our "investment" decisions. You would be making a sector based decision. In other words, he greatly improved his 'base rate' probabilities of investing success by following those rules. Bayes (in green) was sitting was sitting with his back to plain table, with a book and pen. Student of Life - He tends to buy stocks of small, rather than big, companies. This is illustrated by the fact that he was one of the first investors in the UK to have an ISA portfolio worth a million pounds. Another rule he has is that he likes to attend Annual General Meetings of companies in his portfolio, or of companies in which he is considering investing, and to have discussions with directors if he can, so that he has a better understanding of the businesses of those companies and a feel for whether the management is honest and trustworthy. He avoids start-ups and biotech or exploration stocks. This is however much, much lower than lactose intolerance, with 0.09%. This is the base rate fallacy in a nutshell. Tom. Base-Rate Fallacy in Intrusion Detection3. If I was to employ such a strategy, my worry would be that I've essentially replaced one forecasting problem (the stock picking problem) with another almost identical forecasting problem (the sector picking problem). Conditional probability answers the question ‘how does the probability of an event change or the base rate fallacy?" Also I think the stocks of such companies would tend to be less volatile than those of highly-indebted ones, and it is known that low-volatility stocks tend to perform better over the long-run.] Tournesol wrote: "yes but what on earth does any of that have to do with Bayes Theorem? This basically means. View all posts by kilian. It shows how a prior assumption (called prior probability) is updated in a light of new evidence. Tom, Thanks for the feedback - I quite enjoyed writing this one. I concluded that what was needed was a historically successful set (or sets) of screening criteria and an investment approach that suits your personality so you stick with it. Example 1: Even if you are brilliant, you are not guaranteed to be admitted to Harvard: P(Admission|Brilliance) is low, because P(Admission) is low. 2 Conditional Probability. "So in the example given we were directed to consider that although satanists often have certain characteristics their numbers are small. A person receiving a positive test could be around 97.7% confident that it correctly indicates the development of the lactose intolerance. Always good to question your own stock picking skills in my view. The axioms of probability are these three conditions on the function P: 1. He asked his servant (in yellow) to throw a ball on the table and mark the position, where the ball has landed. (GPAs) of hypothetical students. Spare production capacity was at an all time low. Theorem. Ultimately, most of us are in this game to protect and grow our capital...not to convince ourselves and others that we're great stock pickers! In the Zika example, the rate of infection in the general population is very low, just \(1\%\). We can see that the probability of the woman has cancer is calculated as 7.76%. Understand the base rate fallacy thoroughly. 1 For a more extensive treatment see one of John Kruschke’s blog posts. This example, I’ve visualized from a video by Veritassium called “The Bayesian Trap”. Footnotes. ( Log Out / At the very least, how else could you improve them but through rigorous and regular assessment? 2 Review of Bayes’ theorem Recall that Bayes’ theorem allows us to ‘invert’ conditional probabilities. What the thread originator was getting at with Bayes was the need to separate the general/shared characteristics of a group or class of objects (their base rate) from the specific differences between individuals. I am not saying that it is easy to figure out sectoral vectors (direction and magnitude of movement). I was using Lord John Lee as an example of someone who been extremely successful at investing over many years, and whose success supports what Tom Firth wrote in that section. In short, it describes the tendency of people to focus on case specific information and to ignore broader base rate information when making decisions involving probabilities. Bayes’ theorem: what it is, a simple example, and a counter-intuitive example that demonstrates the base rate fallacy. [I think this reduces the probability of him selecting a stock that will perform badly in the short-term.] [This must greatly reduce the probability of any companies in his portfolio going bankrupt. As far as I'm concerned, whatever works, works. Does make me think that I am not quite so good a stock picker after all and that Stockrank factors which remove my stock picker logic should be given more prominence. I have already explained why NSA-style wholesale surveillance data-mining systems are useless for finding terrorists. Thus, it is not at all clear that Bayes' theorem deserves the … P( H | E ) = probability of H(ypothesis) given that E(vidence) [so “|” means “given that”] or in other words, the probability that the hypothesis holds, given that the evidence is true. I think you could express the same ideas using the less daunting term 'conditional probability'. If you will allow me to play Devil's advocate for a minute though, how would you say that picking sectors is different from picking stocks? And if oil companies are in the ascendant then you can harvest much of the potential gains without succeeding in picking the very best stock. Christians might possess the same characteristics only rarely but their numbers are big. Economic development was bringing many new consumers into the marketplace. This is the new calculated belief that incorporated the base rate in the calculation. You could if you wished simply buy the sector in toto by using a collective or by buying a basket of shares. There is an old rubric to the effect that it is more important to invest in the right sector than it is to invest in the right stock - and actually that is really a restatement of Bayesian thinking. No shame in hedging your bets, it just helps to take the pressure off your own analysis after all. Intuitively, one might think that it is not much different from the example above. Bayes’ theorem states that: The above looks complicated, so let’s go back a bit. - He prefers conservative, cash-rich companies or those with low levels of debt. ". ... and so he commits himself to committing the base-rate fallacy. [I think another way to look at this rule is he is using negative momentum to make some selling decisions, and it is well known that stocks with recent negative momentum tend to under-perform the market as a whole over the short-term.] My own experience is that it has several times been possible to call the oil sector and to position oneself with advantage. That all makes sense and in particular your 3rd paragraph clarifies nicely. "If you will allow me to play Devil's advocate for a minute though, how would you say that picking sectors is different from picking stocks? A classic explanation for the base rate fallacy involves a scenario in which 85% of cabs in a city are blue and the rest are green. Very interesting read. noted that research on the "base-rate fallacy" used an incomplete Bayesian analysis. This and other experiments led eventually to a mathematical formulation of Bayes theorem. This idea is linked to the Base Rate Fallacy. Change ), You are commenting using your Twitter account. Let’s say we have two events and . I don't want to snark about this I just do not relate what you are saying to the subject under discussion. Worldwide around 90 per 100,000 people are exhibiting this auto-immune disease. [This greatly reduces his transaction costs, and transaction costs act like a tax on performance, so I think this is likely to improve his long-term results.]

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