by Massimo Pigliucci
* The dark side of oxytocin: hormone of love, but also hormone of tribal warfare.
* How do we know if a country is still stuck in the Middle Ages? Apparently, we look at what its lawyers do.
* The ESP debacle shows why Bayesian analysis is superior to frequentism.
* Even Scientific American sometimes manages to make little sense...
* Should members of Congress be more protected from gun violence than the rest of us?
* Once more Jon Stewart proves himself to be the sanest person in America.
* Do philosophers have a particularly hard time with love? Let's philosophize about it.
* The philosophy of the abortion debate, easy, right?
* Talk about a fact free America...
* Silverman, O'Reilly and Colbert: why humor is so much better than vitriol in making the case for atheism.
I was interested in the NYT article on ESP and how it shows anything about frequentism and Bayesian analysis, but it is behind a paywall. Any other option for us poor guys outside the US who are not subscribers?
ReplyDeleteHmm, I can get in by simply registering for the site, without paying. Have you tried that? But maybe rules are different between in/out of US.
ReplyDeleteIt actually worked like you say. Thanks.
ReplyDeleteYour "fact free America" link appears to be deceased.
ReplyDeleteLeo, it looks like the LiveScience site is temporarily down for maintenance. Check again later on.
ReplyDeleteNow I've read the NYT article, and have some comments.
ReplyDelete1. It is surely better to use Bayesian analysis than simple or traditional significance testing.
2. On the other hand, it seems to me a bit confusing to call the said traditional method "frequentism". The reason for this contention I explain in what follows.
Frequentism as a theory of probability is opposed to a subjective notion of probability as a "degree of belief", however that degree is attained. The frequentist would say that what is called probability is the fact that a particular event happens in a certain proportion of observed cases. It is opposed to the subjective theory of probability (De Finetti).
Out degree of belief in a certain outcome might be based on past observed cases, or in whatever other reasons (say, in theoretical reasoning or a priori ideological reasons).
As an aside, this argument suggests also a distinction between a positive notion of probability (what it is, and how it is measured) and a normative one (what action should be taken if you think the probability of an event is p). Degrees of belief are involved in the latter, but not necessarily in the former. Bayesian analysis may be involved in both: in positive probability it just defines conditional probability (probability of A or not-A, if B is known). Bayesian probabilities, both prior or posterior, can in principle be based on anything, but if probability is to be devoid of metaphysical overtones it should be based on the frequency of observed phenomena (or in some cases in theoretical reasoning, such as "What's the probability of heads in a perfectly balanced coin of negligible thickness").
I'll continue in a separate comment to avoid surpassing the maximum length allowed.
(continued)
ReplyDeleteThis approach means also that probability is computed from collections or groups, and cannot be applied to individuals except as members of such collectives. For instance, suppose science says the probability of living another five years after a heart transplant is p. This is the result of a (relatively large) number of transplant cases observed in the past. The probability can be Bayesian: what if the person is obese? In this case, p would mean the probability of 5-year survival for obese people with a transplanted heart. But that does not change the fact that p is just a relative frequency.
Now comes the next candidate for transplant. What is "her" probability? We assign her the known probability as observed in previous cases,
p, depending on her other characteristics (age, obesity, smoking record, and the like.
Now, in practice the outcome for her would be either "survived" or "died" (some may be censored if they die from other causes before 5 years). She would never achieve an outcome of p (being p% dead is impossible). In fact, whatever happens to her is compatible with the p probability: he may die from heart complications, survive, or be killed in a car accident. In other words, her outcome is perfectly indeterminate, just like the next coin may turn up heads or tails (i.e. will collapse to p=1 or p=0, without any intermediate possibility). We assign her a fractional probability p only insofar as she is a member of the group on which the probability (relative frequency) was based, but can tell nothing about her particular fate.
One can predict on the basis of probabilities, of course, but the prediction cannot be falsified by any individual outcome. The prediction is about collections of future cases (a number of future transplants), not about any individual case.
The only role of an individual outcome is that it is useful to update the given probability. Adding the case of this patient to the data base would possibly alter the p probability, albeit very slightly; as more cases accumulate p can be more significantly updated, in true Bayesian fashion, but this has nothing to do with the frequentist-subjective ways of defining probability: we have always kept this discussion in frequentist (and Bayesian) terms.
Now, as a rule for decision, frequentist-Bayesian rules are good, for they are all we have before the fact. But our success in making those decisions can only be judged for the group as a whole, not for any individual. Perhaps some cases who were not transplanted may have been helped by the transplant, and perhaps some transplanted cases were hopeless anyway and did not postpone death significantly by having undergone the transplant. We simply do not know. But a rule that minimizes failures for the collective of cases is surely a good rule.
Philosophize about love? Why certainly. Don't mind if I do.
ReplyDeleteLove is yet another pillar of the pervasive culture of delusion in which are immersed (states, money and religion being the other pillars). Despite the nearly metaphysical power that writers wish to ascribe to it it is nothing more or less than the relationship that you have with the image of something in your mind. Agreement of that image with an actual material object is convenient, but by no means necessary. It is by no means something shared by two people as the poets would imply. Two people means two different loves. This is how unrequited love is possible and how people can have a deep and abiding love for a celebrity who doesn't even know their admirer exists.
On the face of it even knowing another person is an iffy proposition. What you know of others is gathered from a limited number of experiences and collected by an inherently faulty memory. Even if you observed them 24/7 you still wouldn't know what they were thinking. So since you can't really know, let alone love, another person what is it that people do love when they use that word? I think what they really mean is something more along the lines of 'I love the way you make me feel.'
This image/reality problem is also why I think that people's love for their pets is so very strong. Your image of the animal is quite likely to be very close to the actuality of the animal. Few pets are full of hidden agendas, deception and unpleasant surprises as people are. You pretty much know if dogs or cats like you right away.
So I guess success at love would be finding someone who agrees well with your image of them and for whose image you have a strong fondness. Likewise their image of you be as accurate as possible and their attachment to it strong.
Good luck.
Oh, but Thameron, don't you know love isn't real love unless it is a mutually respecting, bonding, reciprocating relationship in which two people feel affection for each other without wanting to possess each other? Don't you know that?
ReplyDeleteThe ESP article buttresses the 'science as just another religion' argument. An innocent research paper with results that need to be studied is unwelcome at the gate, not because of bad methods, but bad content.
ReplyDeleteMeanwhile, notice how silent the particle physicists have become in the last 20 years in support of unidirectional temporal flow.
Dave, c'mon, the article is based on bad (statistical) methods. And it does make a lot of sense (particularly from a Bayesian perspective!) to be extremely suspicious of any paranormal claim, given the abysmal record of such claims (exceedingly low priors).
ReplyDeleteBad idea to shorten link URLs in your posts.
ReplyDeleteI always want to see where the piece you're recommending is published before deciding whether to click, and the link URL provides me with just this info.
Pretty sure other people do the same.
Now back to my lurker's corner...
I know, on the other hand, shortened links allow me to see how many people follow through...
ReplyDeleteMassimo,
ReplyDeleteat the beginning of this thread I posted a comment about your apparent conflation of statistical significance and probability "frequentism" as opposed to Bayesian reasoning. I surmised you can be Bayesian and frequentist, since these concepts refer to altogether different dimensions of probability theory. I'd like to learn your take on that.
Hector,
ReplyDeletewhile the issue of statistical significance is indeed conceptually separate, "frequentism" is the term usually applied to a family of classic statistical approaches, as distinct from Bayesianism, so I don't think there was any conflation on my part.
A terminological ambiguity, then, is conveyed by that use of the term. For the use of frequentism referring to the concept of probability as the relative frequency of an observed event a classic reference is J.Neyman (1977) and the early Neyman & Pearson (1928). A classic subjective probability theorist is Bruno De Finetti (http://www.brunodefinetti.it/). Gerd Gigerenzer underscores, in his analysis of "bounded rationality", the importance of distinguishing frequentist and subjective presentations of statistical problems (it seems that people are "naturally frequentist", and thus understand probability problems better when they are presented in a frequentist manner: see Gigerenzer 2000 and Gigerenzer & Selten 2002).
ReplyDeleteRefs
Neyman J. 1977. Frequentist probability and frequentist statistics. Synthese, 36:97-131.
Neyman J. and E. S. Pearson, 1928. On the use and interpretation of certain test criteria for purposes o statistical inference. Biometrika, 20A:175-240.
Gigerenzer, Gerd, Adaptive Thinking: Rationality in the Real World. Oxford Univ Press.
Gigerenzer, Gerd & Reinhard Selten eds, 2002. Bounded Rationality: The Adaptive Toolbox. The MIT Press.
Really it doesn't help at all to justify abortion by saying that the right to life applies only to persons ( ..."Secondly, you have to be a Pirate"), since the category of 'person' is a legal definition subject to arbitrary manipulation. Ad hoc, that is to say. We wish to 'abort' embryos but not 'murder' infants, so the latter are declared to be 'persons' but the former are not.
ReplyDeleteBesides, (..."And thirdly, the code is more what you'd call ... guidelines"), many categories of 'person' are subject to socially approved persecution. Such as casualties from high speed chases and warrant service, not to mention civilians standing too close to a "just war". Or, reaching just a little, include death by denial of sustenance, shelter, or care.
Personally I think it would be nice if all that sort of thing could be put in the past. One step at a time, eh?
In re humor v. vitriol--and at the risk of undue equine torture--please note, all, that the humor in question depended directly, in time and logic, on the alleged vitriol. Just saying....
ReplyDeleteMassimo,
ReplyDeleteWhat does it mean for one statistical method to be superior to another? Is this like debates over voting systems? Is this math, philosophy, objective, subjective, or what?
Max, there is a large literature about the differences between frequentist and Bayesian approaches (and also about likelihood approaches, which though technically frequentist actually enjoy several of the advantages of Bayesianism). I think the Bayesian approach is superior for a variety of reasons, one of which is that it doesn't result in the kind of spurious "significant" results that have set off the ESP debacle last week.
ReplyDeleteMassimo,
ReplyDeleteThe Bayesian approach makes more sense to me too because it seems more rigorous, but is that like arguing that Condorcet voting is superior to plurality voting, or naturalism is superior to supernaturalism, or Firefox is superior to Internet Explorer, or Star Trek is superior to Star Wars?
Max, if those are the choices, I'd say that it is more like Firefox vs IE: they both get the job done, most of the time, but one is undeniably better than the other.
ReplyDelete