# base rate fallacy bayes

In retrospect perhaps I should have opted for plain old clarity instead. A person receiving a positive test could be around 97.7% confident that it correctly indicates the development of the lactose intolerance. I'm not saying I disagree, I'm just curious as to how you (or anyone else?) When given relevant statistics about GPA distribution, students tended to ignore them if given descriptive information about the particular student even if the new descriptive information was obviously of little or no relevance to school performance. 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! Base rate fallacy. Base Rate Fallacy。 The Base Rate in our case is 0.001 and 0.999 probabilities. By your logic almost all successful investors could be said to be applying Bayes Theory. 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. Tom, Tom, Why are doctors reluctant to randomly test or screen patients for rare conditions? 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. If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). Change ), You are commenting using your Facebook account. 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. Footnotes. Tournesol wrote: "yes but what on earth does any of that have to do with Bayes Theorem? Bayesian models are more intuitive to correctly specify than frequentist tests. Always good to question your own stock picking skills in my view. However, to do that, we need to include the possibility that we could be one of the rare false positives. Base rate fallacy. Amazon through www.audible.co.uk have a good selection of investment audiobooks for instant download to a smartphone - Great for listening to in the car on a long journey. Get an intuition of what Bayes theorem is: One great example of the Bayes theorem and how it impacts our daily decision making is the base rate fallacy. Is it easier? Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. 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. Have a good evening, The Bayesian Doctor will calculate the updated belief based on this information using Bayes Theorem and update the chart of 'Updated Beliefs'. - 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. (P(S) = 100%. A generic information about how frequently an event occurs naturally. Impact on Intrusion Detection Systems4. 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. You would be making a sector based decision. 5. Yes great article. An example is scrutiny (and subsequent demolition) of Fortune 500 companies who hire or fire their CEO's for what turns out to be random short term financial success of failure. Birn-baum showed that behavior described as "ne-glect of base rate" may be consistent with ra-tional Bayesian utilization of the base rate. Base Rate Fallacy。 The Base Rate in our case is 0.001 and 0.999 probabilities. yes but what on earth does any of that have to do with Bayes Theorem? ( Log Out / 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. Why do knowers of Bayes's Theorem still commit the Base Rate Fallacy? Generally, when you see evidence, it can partly confirm your hypothesis, but at the same time also partly confirm another (competing) hypothesis. But, the big but in general, hospitals double check some positive results and you therefore could trust your hospitals. "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? In other words, he greatly improved his 'base rate' probabilities of investing success by following those rules...." [Again, this reduces the chances of fraud by the management at the expense of shareholders.] Someone else who fancies themselves at stock picking would be sticking individual companies under their microscope and assessing their potential as individuals. Why would I be more likely to get it right just because I'm analysing a different aspect of the future? 8.5 The Base Rate Fallacy. I really think you are talking about something quite unrelated to the subject under discussion here. 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). Why do knowers of Bayes's Theorem still commit the Base Rate Fallacy? 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). 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. I'd look at things from a different angle. [Again I think this must improve the probability of out-performance by those stocks of the market as a whole.] This and other experiments led eventually to a mathematical formulation of Bayes theorem. 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.] I think his use of the above rules over the years must have greatly improved the 'conditional probabilities' [which could, in principle, be calculated mathematically using Bayes Theorem] of him constructing portfolios of stocks that significantly out-performed the FTSE All Share index. This is the new calculated belief that incorporated the base rate in the calculation. General explanation from Wikipedia:. The axioms of probability are mathematical rules that probability must satisfy. 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. noted that research on the "base-rate fallacy" used an incomplete Bayesian analysis. Why are spam filters claimed to be so accurate and yet mess up so often? 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. Is it easier? Bayesian inference tells us what we want to know. Etc etc etc. https://www.gigacalculator.com/calculators/bayes-theorem-calculator.php Pretty much any house builder you bought a few years ago would have done extremely well and if you knew the sector was undervalued, you could have saved yourself a lot of effort by just buying a basket of them. 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. Which might also strengthen the case for IT's or OEICs or ETF's which provide broad coverage of target sectors. Let’s say we have two events and . For manyyears, the so-called base rate fallacy, with its distinctive name and arsenal of catchy Conclusion5. I am familiar with Bayes theorem and I am a big fan of StockRanks but I hadn't made the connection. So we are restricting our view to where the evidences holds. One night, a cab is involved in a hit and run accident. 2. By looking in the table we can simply extract the data: posterior = (prior * probability of prior given new evidence) / all evidence. 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! 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. In relation to stockpicking I am reminded of the book, "Simple, But Not Easy" - Stockpicking is simple but its not easy to be successful. 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]: 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? Such a statement would be so broad and so nebulous as to be of no value. - He prefers to hold stocks for many years, rather than regularly 'churning' his portfolio, and he lets profitable holdings run. 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. In the taxicab example, the base rate for blue cabs was \(15\%\). Let’s suppose that there is a test for telling you if you will develop lactose intolerance in your life. Interesting, thanks for getting back to me. or the base rate fallacy?" This means that the odds are still overwhelmingly in favour of John being a Christian. 2 Conditional Probability. The rate at which something happens in general is called the base rate. Hi Ian, The probability of every event is at least zero. PKA 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! [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.] 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. Understand the base rate fallacy thoroughly. A recent opinion piece in the New York Times introduced the idea of the “Base Rate Fallacy.”. 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. We are told that if a person is actually drunk, the test will indicate so 100% of the time but, in addition to this, 5% of people tested will display a false positive – the test says they are drunk when they…. Conclusion According to Wikipedia (again) 65 % of people experience some form of lactose intolerance (P (Li) ) . Our intuition about what is, or is not evidence, and what is strong versus weak evidence, can be terribly wrong (see, for instance, the base rate fallacy). Ask Question Asked 6 years, 3 months ... ("prevalence" or base rate probability). Hope that makes sense. A really excellent and thought provoking piece, thank you. Bayes’2. General explanation from Wikipedia: When the incidence, i.e. 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. Although John Lee obviously has great skill as a stock-picker, I think it is very interesting [in the light of this excellent article by Tom Firth on Bayes Theorem and conditional probability] how John Lee has increased the odds of long-term success by the rules he uses to reduce the size of the pool of stocks that he picks from. This video by Julia Galef explains more about how you can use Bayes’ theorem, not just to avoid the base-rate fallacy, but also to improve your thinking more generally. Thanks for the book recommendation, had a quick look on Amazon and it looks like an interesting read. Here’s a more formal explanation:. So the learning I take from that is to spend more time choosing sectors than identifying individual stocks. Existing consumers were increasing their consumption. Bayes’ theorem was developed by Rev. Bayesian inference includes conditional probability. 1 For a more extensive treatment see one of John Kruschke’s blog posts. If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). One great example of the Bayes theorem and how it impacts our daily decision making is the base rate fallacy. Base-Rate Fallacy in Intrusion Detection 4. When evaluating the probability of an event―for instance, diagnosing a disease, there are two types of information that may be available. 47.37% (90 / (90 + 100)). I found it a bit confusing when I first read it, because I had wrongly assumed from the title that it is about the Bank of England's base rate, but of course it is nothing to do with that! 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. 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. support the ongoing hypothesis or refute the held beliefs. Christians might possess the same characteristics only rarely but their numbers are big. ( Log Out / The problem is the broader the asset the more efficient the market and the harder it is to do selection... or should we all trade currencies? 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. Population growth was strong. But if the Base Rate is higher, it is well above zero. 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. ". In the appendix we work a similar example. What I'm trying to say is that if builders or banks are in a period of decline then the answer is to avoid those sectors not to invest time and energy trying to pick the best stocks therein. 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. I think that is the rational response to the Bayesian insights. He asked his servant (in yellow) to throw a ball on the table and mark the position, where the ball has landed. Better still when my logic and high Stockrank numbers happen to coincide, or is this just another random event? 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. If so, why? Behavioral and brain sciences, 19(1), 1-17. That's not to say that I don't pick shares too because that is part of the fun of investing, but picking them from a pre-selection of shares that meet your criteria, does give an added confidence factor. Bayes’ theorem: what it is, a simple example, and a counter-intuitive example that demonstrates the base rate fallacy. If house building is the place to be then it's more important to capture the sectoral gains than it is to agonise about which individual stock is best. Tom, thanks for an interesting and useful article. The structure of this problem is the same as that of the base rate fallacy. Base rate fallacy/false positive paradox is derived from Bayes theorem. This is however much, much lower than lactose intolerance, with 0.09%. 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). Tom, Thanks for the feedback - I quite enjoyed writing this one. Again I think this must improve the probability of long-term success of the stocks in his portfolio.] 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). 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. 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. Christians might possess the same characteristics only rarely but their numbers are big. Bayes' theorem for the layman. Bayes noted each new information in his book and realized, that he was able to predict, where the very first ball has fallen simply based on the descriptions of where the other balls have fallen. These are most easily described and understood with an example, which I have shamelessly sourced from Wikipedia. I do not claim any generalised success in other sectors but I'm working on it. The base-rate fallacy only occurs with frequentist methods because they cannot use prior information in a straightforward way. Now, lets say, that a similar test as above is developed for this disease, i.e. generic, general information) and specific information (information pertaining only to a certain case), the mind tends to ignore the former and focus on the latter.. Base rate neglect is a specific form of the more general extension neglect. Consequently there are more Christians who look like satanists than there are satanists who look like satanists. When the incidence, i.e. $\begingroup$ @Semoi The base rate in this case is high enough, and the accuracy of the test good enough (at least when doing it twice in a row) that this doesn't … ( Log Out / 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 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. - 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). You could if you wished simply buy the sector in toto by using a collective or by buying a basket of shares. Quite a few of his examples relate to gambling, but they could equally as well be attributed to our "investment" decisions. I came across the US Guru screens on AAII whose performance data goes back 10 years or more: http://www.aaii.com/stock-screens?a=menubarHome - Click on the different year tags for % gain rankings. If we look at the investment process through this probabilistic lens, what can consideration of base rates and Bayes’ theorem offer us? Thomas Bayes and was first published in 1763, 2 years after his death. [This aligns the interests of the management with those of the shareholders and reduces the chances of fraud by the management. Base rate fallacy example. 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. However, by thinking in terms of the Bayes factor, we can check our intuition, and use evidence much more effectively. 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. Ask Question Asked 6 years, 3 months ... ("prevalence" or base rate probability). 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. 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. 2.1 The base rate fallacy Base-Rate Fallacy in Intrusion Detection3. The English statistician Thomas Bayes has done an interesting experiment on how to visualize that. Empirical research on base rate usage has been domi nated by the perspective that people ignore base rates and that it is an errorto do so. - He tends to buy stocks of small, rather than big, companies. Be able to organize the computation of conditional probabilities using trees and tables. In fact it might be sensible to buy baskets of stocks in the chosen sector rather than just one or two. 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. 2.1 The base rate fallacy. Be able to use Bayes’ formula to ‘invert’ conditional probabilities. I think you could express the same ideas using the less daunting term 'conditional probability'. Worldwide around 90 per 100,000 people are exhibiting this auto-immune disease. View all posts by kilian. Change ), How to do Science: Bayes Theorem and the base rate fallacy, Distinction between Frequentist and Bayesian Approaches, being identified positive, given that you’re sick, being identified positive, given that you not carry the disease, being identified negative, while not carrying the disease, being identified negative, but actually having the disease. Terrorists, Data Mining, and the Base Rate Fallacy. This is where we find out that our minds are poorly primed to deal intuitively with probabilistic reasoning. 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. It is turning out to be the same market beating success story in the UK with many of the Stocko Guru and Stockrank screen selections to date. Change ), You are commenting using your Google account. Suppose you came to the realisation that the oil sector was poised to outperform. That all makes sense and in particular your 3rd paragraph clarifies nicely. 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 %). [Small companies tend to perform better over the long-run than larger ones, although that is not the case in every year.] People tend to simply ignore the base rates, hence it is called (base rate neglect). It is remarkable just how many of these US "Guru" screen selections have beaten the US market, without direct human intervention. Consequently there are more Christians who look like satanists than there are satanists who look like satanists" But if the Base Rate is higher, it is well above zero. In the Zika example, the rate of infection in the general population is very low, just \(1\%\). Lets see how that looks like, by comparing a rare disease (Multiple sclerosis) with a more common disease (lactose intolerance, technically not a disease). When the incidence, i.e. In fact, with every ball and new information, Bayes was able to further narrow down the position of the first ball. 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. I also recommend: Reminisences of a Stockmarket Trader, One up on Wall St and Where are the Customers Yachts, in particular. 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. 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. He says this is a way of limiting the size of his loss if he has made a bad selection of a particular stock, thereby preserving capital for better use elsewhere. ... and so he commits himself to committing the base-rate fallacy. The base rate fallacy and its impact on decision making was first popularised by Amos Tversky and Daniel Kahneman in the early 1970’s. … 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. 2 Review of Bayes’ theorem Recall that Bayes’ theorem allows us to ‘invert’ conditional probabilities. 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 .

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