# base rate fallacy bayes

(P(S) = 100%. Why are doctors reluctant to randomly test or screen patients for rare conditions? 5. Thanks - my apologies for the confusion! One criticism or thing to notice, is that the whole calculation is dependent on the “prior”, the starting hypothesis, that is waiting to be updated by the new evidence. I have already explained why NSA-style wholesale surveillance data-mining systems are useless for finding terrorists. 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). If so, why? 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. He avoids start-ups and biotech or exploration stocks. Let A and B be events. So we are restricting our view to where the evidences holds. Base-Rate Fallacy in Intrusion Detection3. Seems to me that your thought process leads to the idea of emulating investment heroes - "What would Warren Buffett do?" Birn-baum showed that behavior described as "ne-glect of base rate" may be consistent with ra-tional Bayesian utilization of the base rate. When the incidence of a disease in a population is low, unless the test … Fill in your details below or click an icon to log in: You are commenting using your WordPress.com account. General explanation from Wikipedia: When the incidence, i.e. They know about it. We write that the probability of the event is . 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. In the appendix we work a similar example. Bayesian inference includes conditional probability. Footnotes. According to Wikipedia (again) 65 % of people experience some form of lactose intolerance (P (Li) ) . By the way, I thought that what you said here: Why would I be more likely to get it right just because I'm analysing a different aspect of the future? 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. I am familiar with Bayes theorem and I am a big fan of StockRanks but I hadn't made the connection. I cannot find any of that reflected in your discussion of John Lee's approach that will help others to emulate it. Why would I be more likely to get it right just because I'm analysing a different aspect of the future? 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. 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. The base rate fallacy and its impact on decision making was first popularised by Amos Tversky and Daniel Kahneman in the early 1970’s. Again I think this must improve the probability of long-term success of the stocks in his portfolio.] 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. 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. Impact on Intrusion Detection Systems4. This basically means. This is the base rate fallacy in a nutshell. Tournesol wrote: "yes but what on earth does any of that have to do with Bayes Theorem? 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. 47.37% (90 / (90 + 100)). In the taxicab example, the base rate for blue cabs was \(15\%\). I am not saying that it is easy to figure out sectoral vectors (direction and magnitude of movement). 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. … There is no such thing as a negative probability.) However, by thinking in terms of the Bayes factor, we can check our intuition, and use evidence much more effectively. Bayesian inference tells us what we want to know. So stockpicking for me its understanding that I have all the human bias's and need all the help I can get! A really excellent and thought provoking piece, thank you. 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. - He tends to buy stocks of small, rather than big, companies. ( Log Out / 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. In other words, he greatly improved his 'base rate' probabilities of investing success by following those rules. Bayes’Theorem and Base-Rate FallacyTheorem and Base-Rate Fallacy 3. The probability of the entire outcome space is 100%. 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. When the incidence, i.e. Jun 8, 2020 epidemiology. We can avoid this fallacy using a fundamental law of probability, Bayes’ theorem. The base rate fallacy reconsidered: Descriptive, normative, and methodological challenges. I really think you are talking about something quite unrelated to the subject under discussion here. 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! support the ongoing hypothesis or refute the held beliefs. 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 fact, each new experiment and new observation (given that the experimental parameters allow a deduction of a new direction) updates our beliefs, i.e. Cheat Sheets for Computational Biochemistry, "Once you know something, it's difficult to imagine oneself not knowing it.". We have been oversold on the base rate fallacy in probabilistic judgment from an empirical, normative, and methodological standpoint. Economic development was bringing many new consumers into the marketplace. We can see that the probability of the woman has cancer is calculated as 7.76%. A witness claims the cab was green, however later tests show that they only correctly … I also recommend: Reminisences of a Stockmarket Trader, One up on Wall St and Where are the Customers Yachts, in particular. 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. But, the big but in general, hospitals double check some positive results and you therefore could trust your hospitals. [I think this reduces the probability of him selecting a stock that will perform badly in the short-term.] By looking in the table we can simply extract the data: posterior = (prior * probability of prior given new evidence) / all evidence. So the learning I take from that is to spend more time choosing sectors than identifying individual stocks. Suppose you came to the realisation that the oil sector was poised to outperform. 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. [Again I think this must improve the probability of out-performance by those stocks of the market as a whole.] One night, a cab is involved in a hit and run accident. Base rate fallacy/false positive paradox is derived from Bayes theorem. [This must greatly reduce the probability of any companies in his portfolio going bankrupt. Bayes’2. This updated belief (the resulting posterior probability) incorporates all the evidence of that claim. - 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. That all makes sense and in particular your 3rd paragraph clarifies nicely. [Small companies tend to perform better over the long-run than larger ones, although that is not the case in every year.] Where do you stop with this line of thinking though? Tom. ( Log Out / 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?”. This equation is completely fine like it this, but let me expand on P(E), the probability of seeing the evidence, a little bit more. Thus, it is not at all clear that Bayes' theorem deserves the … 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]: 2.1 The base rate fallacy This is where we find out that our minds are poorly primed to deal intuitively with probabilistic reasoning. You could if you wished simply buy the sector in toto by using a collective or by buying a basket of shares. The base-rate fallacy only occurs with frequentist methods because they cannot use prior information in a straightforward way. The Bayesian Doctor will calculate the updated belief based on this information using Bayes Theorem and update the chart of 'Updated Beliefs'. 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. If so, why? 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. Bayes’ theorem has been a controversial idea during the development of statistical reasoning, with many authorities dismissing it as an absurdity. The axioms of probability are mathematical rules that probability must satisfy. Hi Ian, Obviously you would want to invest in companies in that sector. Thanks, Why do knowers of Bayes's Theorem still commit 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. - 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). 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. 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. For manyyears, the so-called base rate fallacy, with its distinctive name and arsenal of catchy After having received the test result (new evidence), we can update our belief by this new evidence. A person receiving a positive test could be around 97.7% confident that it correctly indicates the development of the lactose intolerance. Using Baye's theorem, we get actual probabilities of competing hypotheses. 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. ( Log Out / Let’s say we have two events and . The probability of every event is at least zero. I do not claim any generalised success in other sectors but I'm working on it. Answer to the Thought Experiment: The exact answer to this problem depends upon what percentage of the population is homosexual. Let P(A) denote the probability of the event A. 1. [Again, this reduces the chances of fraud by the management at the expense of shareholders.] Some assessments use a statistical ‘base rate’ as the prior probability. Good luck with your investing, If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). Etc etc etc. 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. A generic information about how frequently an event occurs naturally. 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. 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. (For every event A, P(A) ≥ 0. People tend to simply ignore the base rates, hence it is called (base rate neglect). Tom Firth's article above has a section entitled "Applying the Theory". 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. Quite a few of his examples relate to gambling, but they could equally as well be attributed to our "investment" decisions. Change ), You are commenting using your Google account. Here’s a more formal explanation:. Thanks for the book recommendation, had a quick look on Amazon and it looks like an interesting read. 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. If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). 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! Tom, Tom, He asked his servant (in yellow) to throw a ball on the table and mark the position, where the ball has landed. 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 %). 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. 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. ( Log Out / 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. All the best, Bayes’ theorem states that: The above looks complicated, so let’s go back a bit. medical tests, drug tests, etc. Better still when my logic and high Stockrank numbers happen to coincide, or is this just another random event? The base rate fallacy is also known as base rate neglect or base rate bias. So in the example given we were directed to consider that although satanists often have certain characteristics their numbers are small. 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. In retrospect perhaps I should have opted for plain old clarity instead. Example 1 given on the Wikipedia page is clear and easy to picture. The base rate fallacy is a specific mistake of this type, that is, a failure to use all relevant information in an inductive inference. 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 that case, each new ball (new information) updated his belief. 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). Ian, P.S. This and other experiments led eventually to a mathematical formulation of Bayes theorem. No shame in hedging your bets, it just helps to take the pressure off your own analysis after all. Tom, Thanks for the feedback - I quite enjoyed writing this one. You would be making a sector based decision. Of course, John Lee's rules are not the only way to do that. I chose the title because the dash of alliteration made it sound punchy (at least in my mind...). Christians might possess the same characteristics only rarely but their numbers are big. 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! Is it easier? 2 Conditional Probability. Be able to use Bayes’ formula to ‘invert’ conditional probabilities. 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.

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