PKA Yes great article. In relation to stockpicking I am reminded of the book, "Simple, But Not Easy" - Stockpicking is simple but its not easy to be successful. By the way, I thought that what you said here: Tom, Thanks for the feedback - I quite enjoyed writing this one. Theorem. 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. 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. or the base rate fallacy?" Here’s a more formal explanation:. This and other experiments led eventually to a mathematical formulation of Bayes theorem. Base Rate Fallacy。 The Base Rate in our case is 0.001 and 0.999 probabilities. 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. 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 %). If a woman has breast cancer, the probability that she tests positive is 90% ("sensitivity" or reliability rating). Bayes’ theorem: what it is, a simple example, and a counter-intuitive example that demonstrates the base rate fallacy. This is the new calculated belief that incorporated the base rate in the calculation. Impact on Intrusion Detection Systems4. This finding has been used to argue that intervi… 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. Thomas Bayes and was first published in 1763, 2 years after his death. Base-Rate Fallacy in Intrusion Detection 4. 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. "So in the example given we were directed to consider that although satanists often have certain characteristics their numbers are small. You could if you wished simply buy the sector in toto by using a collective or by buying a basket of shares. This is the base rate fallacy in a nutshell. 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! Bayes’ theorem states that: The above looks complicated, so let’s go back a bit. Economic development was bringing many new consumers into the marketplace. Tom, ( Log Out /  (For every event A, P(A) ≥ 0. 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. 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”. Consequently there are more Christians who look like satanists than there are satanists who look like satanists. 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. I'm not saying I disagree, I'm just curious as to how you (or anyone else?) 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. - He tends to buy stocks of small, rather than big, companies. Worldwide around 90 per 100,000 people are exhibiting this auto-immune disease. The base rate fallacy is a specific mistake of this type, that is, a failure to use all relevant information in an inductive inference. Let P(A) denote the probability of the event A. Be able to use Bayes’ formula to ‘invert’ conditional probabilities. Answer to the Thought Experiment: The exact answer to this problem depends upon what percentage of the population is homosexual. However, by thinking in terms of the Bayes factor, we can check our intuition, and use evidence much more effectively. 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. Generally, when you see evidence, it can partly confirm your hypothesis, but at the same time also partly confirm another (competing) hypothesis. This is however much, much lower than lactose intolerance, with 0.09%. I came across the US Guru screens on AAII whose performance data goes back 10 years or more: - Click on the different year tags for % gain rankings. A person receiving a positive test could be around 97.7% confident that it correctly indicates the development of the lactose intolerance. 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. 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). If we look at the investment process through this probabilistic lens, what can consideration of base rates and Bayes’ theorem offer us? 2. When the incidence of a disease in a population is low, unless the test … Bayes’ theorem was developed by Rev. Good luck with your investing, 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. Existing consumers were increasing their consumption. Bayes’ theorem has been a controversial idea during the development of statistical reasoning, with many authorities dismissing it as an absurdity. Interesting, thanks for getting back to me. Fill in your details below or click an icon to log in: You are commenting using your account. Why would I be more likely to get it right just because I'm analysing a different aspect of the future? ( Log Out /  Why do knowers of Bayes's Theorem still commit the Base Rate Fallacy? The structure of this problem is the same as that of the base rate fallacy. Namely, if the Base rate is low, say 0.1%, the probability is practically zero. 1 For a more extensive treatment see one of John Kruschke’s blog posts. Applications and examples. You would be making a sector based decision. Change ), You are commenting using your Twitter account. In fact it might be sensible to buy baskets of stocks in the chosen sector rather than just one or two. ". In this case, throwing a coin will more accurately tell, if you have the disease. 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?”. So we are restricting our view to where the evidences holds. Consequently there are more Christians who look like satanists than there are satanists who look like satanists" 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. "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...." In the appendix we work a similar example. Thus, it is not at all clear that Bayes' theorem deserves the … As far as I'm concerned, whatever works, works. Tom. 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. Why would I be more likely to get it right just because I'm analysing a different aspect of the future? We write that the probability of the event is . Why are doctors reluctant to randomly test or screen patients for rare conditions? Base Rates and Bayes’ Theorem. 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. 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. 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. I am not saying that it is easy to figure out sectoral vectors (direction and magnitude of movement). [I think this reduces the probability of him selecting a stock that will perform badly in the short-term.] 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. 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. Conclusion Hi Ian, 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? 2.1 The base rate fallacy Base rate fallacy. In retrospect perhaps I should have opted for plain old clarity instead. When the incidence of a disease in a population is low, unless the test … In the Zika example, the rate of infection in the general population is very low, just \(1\%\). Why are spam filters claimed to be so accurate and yet mess up so often? If you are not comfortable with Bayes’ theorem you should read the example in the appendix now. I think that greatly improved the conditional probabilities (which could in principle be calculated using Bayes Theorem if one had all the data) of successful outcomes from his portfolios over the long-term. [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.] 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. But, the big but in general, hospitals double check some positive results and you therefore could trust your hospitals. 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. Someone else who fancies themselves at stock picking would be sticking individual companies under their microscope and assessing their potential as individuals. (The right sector is the one with the most favourable base rate. ) Base rate fallacy. The base-rate fallacy only occurs with frequentist methods because they cannot use prior information in a straightforward way. Base rate fallacy example. However, to do that, we need to include the possibility that we could be one of the rare false positives. This idea is linked to the Base Rate Fallacy. Again I think this must improve the probability of long-term success of the stocks in his portfolio.] 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. Namely, if the Base rate is low, say 0.1%, the probability is practically zero. Always good to question your own stock picking skills in my view. All the best, 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. So in the example given we were directed to consider that although satanists often have certain characteristics their numbers are small. Such a statement would be so broad and so nebulous as to be of no value. Bayes' theorem for the layman. One great example of the Bayes theorem and how it impacts our daily decision making is the base rate fallacy. This means that the odds are still overwhelmingly in favour of John being a Christian. … 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.] 7. In the taxicab example, the base rate for blue cabs was 15% 15 %. I also recommend: Reminisences of a Stockmarket Trader,  One up on Wall St and Where are the Customers Yachts, in particular. Cheat Sheets for Computational Biochemistry, "Once you know something, it's difficult to imagine oneself not knowing it.". 2. Which might also strengthen the case for IT's or OEICs or ETF's which provide broad coverage of target sectors. 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! 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. - He prefers conservative, cash-rich companies or those with low levels of debt. 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. Tournesol wrote: "yes but what on earth does any of that have to do with Bayes Theorem? Christians might possess the same characteristics only rarely but their numbers are big. The chance that somethingin the outcome space occurs is 100%, because the outcome space contains ever… 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. After having received the test result (new evidence), we can update our belief by this new evidence. Very interesting read. 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? Example 1 given on the Wikipedia page is clear and easy to picture. 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. Jun 8, 2020 epidemiology. [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.] - 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). We will begin to justify this view today. There is no such thing as a negative probability.) - 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. Let’s say we have two events and . In fact, with every ball and new information, Bayes was able to further narrow down the position of the first ball. 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). really summarised the idea concisely and in very simple language - I may have to borrow your phrasing in the future! Student of Life Some assessments use a statistical ‘base rate’ as the prior probability. As we shall see, assessments that underestimate the importance of a statistical base rate commit the fallacy known as ‘base rate neglect’. We have been oversold on the base rate fallacy in probabilistic judgment from an empirical, normative, and methodological standpoint. 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. 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. - He prefers companies that have had few changes in their directors and few changes in their auditors. 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. 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. 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). I'm read Kahneman so have already grappled with Bayes Theorem and found it fascinating to see how absolutely counter intuitive the outcomes are when it's applied to apparently simple problems. Have a good evening, 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. 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. Hope that makes sense. Terrorists, Data Mining, and the Base Rate Fallacy. But if the Base Rate is higher, it is well above zero. [Again, this reduces the chances of fraud by the management at the expense of shareholders.] These are most easily described and understood with an example, which I have shamelessly sourced from Wikipedia. The axioms of probability are these three conditions on the function P: 1. The probability of the entire outcome space is 100%. The rate at which something happens in general is called the base rate. Bayesian inference includes conditional probability. The English statistician Thomas Bayes has done an interesting experiment on how to visualize that. In other words, he greatly improved his 'base rate' probabilities of investing success by following those rules. 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. 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.