@yudapearl Echoing @f2harrell 's journey from a frequentist to a Bayesian statistician, I am re-posting my journey from a Bayesian to a "Half Bayesian" AI researcher: https://ucla.in/2nZN7IH Readers who have seen it before can just skip, and those who have not, can take this re-posting as a confirmation that I still stand behind every word of my 2001 confession. Mar 27 I improved my second most popular blog article: https://fharrell.com/post/journey #Statistics #bayes Norm Matloff 一啲都唔明 @matloff Even more eloquently written than @f2harrell 's, but still missing the point IMO. The key word in your quote of Savage in the opening statement is "know." If the word is literally true, than none of us frequentists would object (nor would we consider it non-frequentist). Empirical Bayes is fine, for instance. The problem occurs when "know" is replaced by "feel," in which case the analysis becomes subjective and possibly very biased. One can use the data to check frequentist assumptions but one cannot check feelings. Feelings should have no place in scientific research, especially medical research, which is a public good. If someone wants to incorporate their feelings into their own private analysis of the stock market, say, good for them. Judea Pearl @yudapearl · Mar 27 All scientific knowledge is based on some assumptions. Are you proposing to purge science from Bayes analysis? Juan Carlos Silva @chobitoso · Mar 27 I found these discussions somewhat repetitive. Even some frequentist algorithms and interpretations rely on Bayesian analysis. For instance, diagnostic testing is a pure Bayesian exercise. They are not completely independent perspectives. Norm Matloff 一啲都唔明 @matloff · Mar 27 Please explain re diagnostic testing. Juan Carlos Silva @chobitoso · Mar 27 Simultaneous or in tandem?? Still a pure Bayesian exercise… Norm Matloff 一啲都唔明 @matloff · Mar 27 Sorry, I don't know the term. Please explain. Juan Carlos Silva @chobitoso · Mar 27 In epidemiology and other fields, you would classify a patient with a test that has two properties sensitivity and specificity. However these properties are affected by a third variable, the prevalence of the condition. Thus, you need to update the tests results even if you… Post See new posts Conversation Judea Pearl @yudapearl · Mar 27 Echoing @f2harrell 's journey from a frequentist to a Bayesian statistician, I am re-posting my journey from a Bayesian to a "Half Bayesian" AI researcher: https://ucla.in/2nZN7IH Readers who have seen it before can just skip, and those who have not, can take this re-posting as a Show more Quote Frank Harrell @f2harrell · Mar 27 I improved my second most popular blog article: https://fharrell.com/post/journey #Statistics #bayes Norm Matloff 一啲都唔明 @matloff · Mar 27 Even more eloquently written than @f2harrell 's, but still missing the point IMO. The key word in your quote of Savage in the opening statement is "know." If the word is literally true, than none of us frequentists would object (nor would we consider it non-frequentist). Empirical Show more Judea Pearl @yudapearl · Mar 27 All scientific knowledge is based on some assumptions. Are you proposing to purge science from Bayes analysis? Juan Carlos Silva @chobitoso Mar 27 I found these discussions somewhat repetitive. Even some frequentist algorithms and interpretations rely on Bayesian analysis. For instance, diagnostic testing is a pure Bayesian exercise. They are not completely independent perspectives. Norm Matloff 一啲都唔明 @matloff Mar 27 Please explain re diagnostic testing. · Mar 27 Simultaneous or in tandem?? Still a pure Bayesian exercise… Norm Matloff 一啲都唔明 @matloff Mar 27 Sorry, I don't know the term. Please explain. Juan Carlos Silva @chobitoso · Mar 27 In epidemiology and other fields, you would classify a patient with a test that has two properties sensitivity and specificity. However these properties are affected by a third variable, the prevalence of the condition. Thus, you need to update the tests results even if you… Norm Matloff 一啲都唔明 @matloff That's entirely frequentist. It's in Fisher LDA for instance, and it is part of the intercept term in the logit model. It is thus part of the process of estimating from the data, again thoroughly, classically frequentist. Now if the mix in the data is not representative of the population, one can then do "what if" analysis, looking at various cases. That is frequentist as long as one does not model the disease prevalence by a distribution, which becomes subjective. Norm Matloff 一啲都唔明 @matloff · Mar 27 1. I personally do not use (subjective) Bayesian methods. 2. If someone wants to use such methods for their personal, private use, that's fine with me. 3. But (subjective) Bayesian methods should not be used in settings affecting the public, e.g. medical research. Biostatsfun @biostatsfun Mar 27 And the issue raised by Frank is decision making based on p-values. A clinician understands pr(benefit) better than p-values. Norm Matloff 一啲都唔明 @matloff Mar 27 What clinicians understand or not is a whole other interesting topic. :-) Re p-values, DON'T USE THEM. But just because a clinician may "understand" superstition doesn't make it right. Biostatsfun @biostatsfun · Mar 27 But you check prior sensitivity, what’s the issue? How does justifying a prior = frequentist? No, I wouldn’t equate plausibility with feelings. On feelings, I’d trust a physicians “feelings†over my own. Norm Matloff 一啲都唔明 @matloff Mar 27 Fine, but the problem is that one doctor's feelings will be different from another's. That's why it's not scientific. As to checking sensitivity, think of the implication: If one gets essentially the same results with different priors, one is basically back to the frequentist realm. If one gets different results with different priors, then which one is correct? It's all superstition. Judea Pearl @yudapearl Mar 27 All scientific knowledge is based on some assumptions. Are you proposing to purge science from Bayes analysis? Norm Matloff 一啲都唔明 @matloff · Mar 27 Please reread my point about checking assumptions. Dylan Armbruster @dylanarmbruste3 Mar 27 Would you say you lean more towards Frequentist? Norm Matloff 一啲都唔明 @matloff · Mar 27 Not lean towards. 100% for anything that affects the public. · Mar 27 What do you mean. How would you classify yourself then? Norm Matloff 一啲都唔明 @matloff · Mar 27 1. I personally do not use (subjective) Bayesian methods. 2. If someone wants to use such methods for their personal, private use, that's fine with me. 3. But (subjective) Bayesian methods should not be used in settings affecting the public, e.g. medical research. Frank Harrell @f2harrell If you think that Bayesian methods are more subjective than frequentist ones you have not deeply examined frequentist methods. 4:39 AM · Mar 28, 2025 · Norm Matloff 一啲都唔明 @matloff Mar 28 I think this is at least the third time you and I have debated freq. vs. Bayes here on Twitter/X. I've looked deeply at whatever you've brought up, but you now say I've overlooked some points in your newly-expanded article. I will definitely take a look. Frank Harrell @f2harrell Mar 28 This is a bit of an oversimplification, but I don't love Bayes because it's perfect. I love Bayes because of (1) its problem-solving capabilities and (2) frequentist approaches are deeply flawed. Norm Matloff 一啲都唔明 @matloff Mar 27 Even more eloquently written than @f2harrell 's, but still missing the point IMO. The key word in your quote of Savage in the opening statement is "know." If the word is literally true, than none of us frequentists would object (nor would we consider it non-frequentist). Empirical Norm Matloff 一啲都唔明 @matloff OK, I've gone through your article again, and really don't see anything new or view-changing. 90% of it is on the problems with hypothesis testing, which as you know I oppose. (You probably don't remember this, but the very first interaction I had with you was when in some online forum you said that R should not be reporting the "1 star, 2 stars, 3 stars" p-values paradigm, and I said something like "YES!! Finally glad to see someone other than me say it.") A couple of your statements did bring up very important issues (maybe these are among the "new" ones). First, "I came to not believe in the possibility of infinitely many repetitions of identical experiments, as required to be envisioned in the frequentist paradigm." I disagree; on the contrary, we all go through life implicitly making decisions on this basis, whether we are buying insurance, gambling in a casino or whatever. Ask any gambler (I'm not one) what it means that the probability of a payoff is 0.22, and after some thought he/she will indeed talk in terms of repeated trials. Ironically, I hope you will recall that I've often said, "We are all Bayesians." We do have our priors in the numerous decision-making contexts we encounter in life, and informally act on those priors. Again, this is fine with me -- when I said "We all" above, I meant it -- but priors should have no place in scientific research, due to the subjectivity. The other statement in your article that caught my eye concerned frequentists' need "to completely specify the experimental design, sampling scheme, and data generating process..." I would agree, providing one says "to contemplate the implications of" rather than "to completely specify." In fact, there was an example of this earlier in this thread, when we were discussing the overall prevalence of a disease or condition. I said that we must look at the nature of the sampling process, asking whether it is representative of the target population. I then said we might engage in "What if" questions along these lines. Arman Oganisian @StableMarkets Mar 28 How would you answer a doc who wants the probability that the patient in their clinic now will relapse w/n 1 yr? not “the proportion of patients drawn from an infinite subpopulation of patients with the same features as that patient†but the probability for that specific patient. Norm Matloff 一啲都唔明 @matloff · Mar 28 The doc should first say "x% of people like you have a relapse." But a good doctor should add, "Of course, there are many factors underlying this, some of which we know and some we don't know, so it's possible that one of the latter factors makes your case very different." Note that the above applies to both frequentist and Bayesian analyses. The only difference is that the probabilities in the latter case are not real data, just personal hunches that may vary from one doctor to another. An ethical, responsible Bayesian physician should disclose this. Norm Matloff 一啲都唔明 @matloff Going a little further, the doctor should give the patient the probability of a relapse, given those known factors, e.g. age, if it is available. Again, as a patient, this is what I would want, and I'm pretty sure most patients would want it, even if they have no statistics background. Interestingly, that's what the Kaiser system apparently does in reports for blood workups. The "Normal Range" in their graphs is tailored to the patient's age and gender (though it doesn't say so), a nurse told me. Frank Harrell @f2harrell Mar 28 Thanks for all those comments Norm. I have to take issue with your belief that life decisions are made like sampling statisticians think or that gamblers work like that. A resounding "no" to those two. Life and gambling are all about playing the odds in one-time situations. Norm Matloff 一啲都唔明 @matloff Actually, after I posted this tweet, I put the question to several LLMs, asking how people perceive that 0.22 figure for winning a game. All of them cited repeated trials as one of the ways that number is perceived. (The other ways they cited didn't really pertain to the question, for example noting that many people tend to underestimate probabilities.) One can dismiss responses from LLMs -- I didn't ask the LLMs whether they are frequentist or Bayesian :-) -- but still I think their responses here are worth considering, don't you agree? The fact that people are making one-time decisions is not really relevant. People make many many one-time decisions of various kinds over their lifespans, and in principle many of those will involve probabilities of 0.22 or close to it. So there is in fact a long run to consider, even if it consists of a series of one-time settings. not saying that the gambler in this scenario will say, "Hmm, if I play this game many times...†but if you actually ask him/her what the 22% figure means, they will give it some thought and then give some sort of answer based on repeated trials. I think the situation becomes clearer if one asks the same question about expected value, E(X). Putting aside the point that it is misnamed, how is it perceived by people? Of course, most people have never heard the term, but if you explain that it is a long run average based on the probabilities of the events in question, they will immediately understand, and accept that it is a useful quantity to have, even though you bring it up in the context of one-time decision. I would humbly submit that explaining expected value in a Bayesian context is a bit of a challenge. If you have experience with this, I would certainly like to hear it. Frank Harrell @f2harrell Mar 28 No, I don't think that idea of probability in that setting is worth considering. A successful poker player is good at estimating probability of ultimately winning the hand in the one-time situation (one-time because it's not only the cards; it's also the players). Norm Matloff 一啲都唔明 @matloff All true (in the second sentence), but still not addressing the issue of how that player is assessing/interpreting the 0.22 probability. As I said, the one-time nature is irrelevant, as this player, can and I claim does view this in the context of a lifetime of poker with 0.22 probability situations or a lifetime of 0.22 probability events of various kinds (games and nongames). Note the word situations; this player may play with different people, be dealt different hands and so on, but will encounter various situations which, though basically different in lots of ways, still have probabity 0.22 (or near it). In other words, there are repeated trials with the same probability even though the trials are qualitative different. It's like tossing many different but fair coins; we still have probability 0.5 in each toss, even though it's with a different coin each time. Arman Oganisian @StableMarkets Mar 29 What I mean is the doctor didn’t ask for the rate in the subpopulation of patients who share certain features with patient i. They asked for the probability that that particular patient i would relapse. The valid frequentist response doesn’t answer this. Arman Oganisian @StableMarkets · Mar 29 From a Bayes perspective this is a well-defined request for the posterior predictive probability of relapse Y_i given data on previous i-1 subjects the doc has seen: P(Y_i =1 | y_1:i-1 ). It’s not equivocating - just viewing probability as more than just sampling error. Arman Oganisian @StableMarkets · Mar 29 There are (at least?) two valid frequentist responses. 1) Norm’s response, which answers a different question. 2) saying that the probability of relapse is either 100% or 0% and we won’t know for 1 yr - see Blackwell. Going with 2) would ensure no doc works with me ever again! Norm Matloff 一啲都唔明 @matloff Comments: 1. Putting such questions to mathematicians, e.g. Blackwell, is generally counterproductive. They haven't had much if any experience working on real-life problems with real-life data, and tend to appreciate the mathematical eloquence of Bayesian methods. Same BTW for philosophers, specifically meaning @learnfromerror . (She blocks me, BTW, so if you add her to this conversation, I won't see what she says.) 2. As a patient, I want clinicians to give me reasonable assessments. Even if they give me a Bayesian answer, it should mention the role of unknown factors in the studies etc. Earlier in this thread, I talked of "ethical, responsible" physicians, and the same goes for statisticians. To say, "I'll give them an overly simplistic answer, to shut them up," is unethical and irresponsible. 3. It's wrong to say "The probability is either 1 or 0." My usual explanation is to refer to the Monty Hall game show example. (A couple of you brough in game theory; well, this is my game theory. :-) ) Frank Harrell @f2harrell Mar 28 di Finetti is probably a good source here. Norm Matloff 一啲都唔明 @matloff Mar 28 I'd happy to look at a specific reference if you have one, but I must say a priori that I doubt that game theory -- mathematical derivations and proofs -- can shed any light on the topic at hand here, which involves mental perceptions of probability and expected value.