Unfortunately, the human brain does not always deal with evidence properly. In this case, throwing a coin will more accurately tell, if you have the disease. These are most easily described and understood with an example, which I have shamelessly sourced from Wikipedia. Why would I be more likely to get it right just because I'm analysing a different aspect of the future? Bayes’Theorem and Base-Rate FallacyTheorem and Base-Rate Fallacy 3. 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. By your logic almost all successful investors could be said to be applying Bayes Theory. 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. This means that the odds are still overwhelmingly in favour of John being a Christian. This idea is linked to the Base Rate Fallacy. - He prefers companies that have had few changes in their directors and few changes in their auditors. If you are not comfortable with Bayes’ theorem you should read the example in the appendix now. Namely, if the Base rate is low, say 0.1%, the probability is practically zero. A generic information about how frequently an event occurs naturally. … A really excellent and thought provoking piece, thank you. At the very least, how else could you improve them but through rigorous and regular assessment? A person receiving a positive test could be around 97.7% confident that it correctly indicates the development of the lactose intolerance. 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). It is remarkable just how many of these US "Guru" screen selections have beaten the US market, without direct human intervention. Namely, if the Base rate is low, say 0.1%, the probability is practically zero. Behavioral and brain sciences, 19(1), 1-17. Base-Rate Fallacy in Intrusion Detection3. Christians might possess the same characteristics only rarely but their numbers are big. ( Log Out /  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 %). Bayes (in green) was sitting was sitting with his back to plain table, with a book and pen. When the incidence, i.e. Tom, thanks for an interesting and useful article. The base-rate fallacy only occurs with frequentist methods because they cannot use prior information in a straightforward way. 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. People tend to simply ignore the base rates, hence it is called (base rate neglect). Terrorists, Data Mining, and 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. The base rate fallacy reconsidered: Descriptive, normative, and methodological challenges. Bayesian models are more intuitive to correctly specify than frequentist tests. In the taxicab example, the base rate for blue cabs was \(15\%\). Thanks, I really think you are talking about something quite unrelated to the subject under discussion here. You are told that “John is a man who wears gothic inspired clothing, has long black hair, and listens to death metal.”  You are then asked “How likely is it that he is a Christian, and how likely is it that he is a Satanist?”. I am not saying that it is easy to figure out sectoral vectors (direction and magnitude of movement). 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’. 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. Existing consumers were increasing their consumption. Let P(A) denote the probability of the event A. Again I think this must improve the probability of long-term success of the stocks in his portfolio.] 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. The probability of the entire outcome space is 100%. Tom, Tom, noted that research on the "base-rate fallacy" used an incomplete Bayesian analysis. https://www.gigacalculator.com/calculators/bayes-theorem-calculator.php Applications and examples. 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). Where do you stop with this line of thinking though? - He prefers conservative, cash-rich companies or those with low levels of debt. Cheat Sheets for Computational Biochemistry, "Once you know something, it's difficult to imagine oneself not knowing it.". or the base rate fallacy?" This is the base rate fallacy in a nutshell. 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. People tend to simply ignore the base rates, hence it is called (base rate neglect). 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. So the learning I take from that is to spend more time choosing sectors than identifying individual stocks. I chose the title because the dash of alliteration made it sound punchy (at least in my mind...). 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 . 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. Impact on Intrusion Detection Systems 5. This is the new calculated belief that incorporated the base rate in the calculation. Someone else who fancies themselves at stock picking would be sticking individual companies under their microscope and assessing their potential as individuals. 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. Which might also strengthen the case for IT's or OEICs or ETF's which provide broad coverage of target sectors. 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. yes but what on earth does any of that have to do with Bayes Theorem? We have been oversold on the base rate fallacy in probabilistic judgment from an empirical, normative, and methodological standpoint. 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. Be able to use Bayes’ formula to ‘invert’ conditional probabilities. 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. 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. Impact on Intrusion Detection Systems4. 2. In the appendix we work a similar example. P(E|H) is the probability of the evidence if the hypothesis is true. 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. Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. Base rate fallacy example. We will begin to justify this view today. If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). 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). 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). 8.5 The Base Rate Fallacy. Such a statement would be so broad and so nebulous as to be of no value. This and other experiments led eventually to a mathematical formulation of Bayes theorem. 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. Consequently there are more Christians who look like satanists than there are satanists who look like satanists. medical tests, drug tests, etc. Change ), You are commenting using your Google account. However, to do that, we need to include the possibility that we could be one of the rare false positives. ( Log Out /  I'm currently intending to pursue the use of investment trusts to allow me to step back from stock selection and spend more time on sector selection. Bayesian inference tells us what we want to know. If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). If we look at the investment process through this probabilistic lens, what can consideration of base rates and Bayes’ theorem offer us? Interesting, thanks for getting back to me. If so, why? After having received the test result (new evidence), we can update our belief by this new evidence. ". 2 Conditional Probability. 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. When the incidence, i.e. 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. Christians might possess the same characteristics only rarely but their numbers are big. As far as I'm concerned, whatever works, works. One great example of the Bayes theorem and how it impacts our daily decision making is the base rate fallacy. 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. So in the example given we were directed to consider that although satanists often have certain characteristics their numbers are small. [Small companies tend to perform better over the long-run than larger ones, although that is not the case in every year.] Thomas Bayes and was first published in 1763, 2 years after his death. 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. Let’s say we have two events and . 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. The base rate fallacy is a specific mistake of this type, that is, a failure to use all relevant information in an inductive inference. A good stock picker may be better off shorting their sectors to get the relative perf of their stock picks if they want to avoid base risk. Here’s a more formal explanation:. Spare production capacity was at an all time low. All the best, The English statistician Thomas Bayes has done an interesting experiment on how to visualize that. Base Rate Fallacy。 The Base Rate in our case is 0.001 and 0.999 probabilities. 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. 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. Bayes’2. I have already explained why NSA-style wholesale surveillance data-mining systems are useless for finding terrorists. A witness claims the cab was green, however later tests show that they only correctly … 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. Now, lets say, that a similar test as above is developed for this disease, i.e. 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. - He prefers to hold stocks for many years, rather than regularly 'churning' his portfolio, and he lets profitable holdings run. Why do knowers of Bayes's Theorem still commit the Base Rate Fallacy? This is however much, much lower than lactose intolerance, with 0.09%. Why would I be more likely to get it right just because I'm analysing a different aspect of the future? This is where we find out that our minds are poorly primed to deal intuitively with probabilistic reasoning. Using Baye's theorem, we get actual probabilities of competing hypotheses. 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. Very interesting read. 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. Tournesol wrote: "yes but what on earth does any of that have to do with Bayes Theorem? 2.1 The base rate fallacy. 2.1 The base rate fallacy 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. 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. Much of the time it is really difficult to get a read on most of the market. (GPAs) of hypothetical students. However, by thinking in terms of the Bayes factor, we can check our intuition, and use evidence much more effectively. By the way, I thought that what you said here: 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. 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 … - 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. Understand the base rate fallacy thoroughly. He avoids start-ups and biotech or exploration stocks. Bayes’ theorem was developed by Rev. You could if you wished simply buy the sector in toto by using a collective or by buying a basket of shares. A recent opinion piece in the New York Times introduced the idea of the “Base Rate Fallacy.”. $\begingroup$ @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 … support the ongoing hypothesis or refute the held beliefs. This test can predict to 99.9 %, if you will develop this disease (true positive) and the probability of being tested negative, while still developing lactose intolerance is pretty low (false negative: 0.04 %).

base rate fallacy bayes

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