Bayesian networks and causal diagrams

14 October, 2018 at 09:09 | Posted in Theory of Science & Methodology | 11 Comments

36393702Whereas a Bayesian network​ can only tell us how likely one event is, given that we observed another, causal diagrams can answer interventional and counterfactual questions. For example, the causal fork A <– B –> C tells us in no uncertain terms that wiggling A would have no effect on C, no matter how intense the wiggle. On the other hand, a Bayesian network is not equipped to handle a ‘wiggle,’ or to tell the difference between seeing and doing, or indeed to distinguish a fork from a chain [A –> B –> C]. In other words, both a chain and a fork would predict that observed changes in A are associated with changes in C, making no prediction about the effect of ‘wiggling’ A.

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11 Comments

  1. “The … problem solved in this essay [by Bayes] … shews us … what reason there is to think that such recurrency or order is derived from stable causes or regulations in nature, and not from any irregularities of chance.” (Cf https://djmarsay.wordpress.com/bibliography/rationality-and-uncertainty/probability/probability-classics/bayes-essay/ .)

    So, to the extent that Bayesian nets are applications of Bayes’ theory, they clearly do not apply to wiggling, or anything else that changes the regulation of what was observed. If you want to know the effect of wiggling you need to try it and observe the effect. I am not sure I have entirely understood Pearl (https://djmarsay.wordpress.com/bibliography/rationality-and-uncertainty/probability/criticism-of-mathematical-probability/pearls-simpsons-paradox/ ). I see two useful contributions:
    1. A notation for what we ‘do’.
    2. A way of incorporating absolute beliefs about causal independence (such as taking aspirin cannot affect one’s gender).

    This avoids some of the problems with the common-sense notion of ‘causality’. I am not clear if Pearl has render the notion completely harmless. I prefer to rely on what I think I understand. Maybe I should ponder a bit more?

    • Reading the introduction, I think we need to distinguish between two issues. Lars’ criticism of mainstream economists is mainly that they misunderstand the nature of mathematical models. Pearl helps us to avoid misunderstandings of the difference between causality and correlation, but doesn’t seem to address the unavoidable issues with models that Whitehead et al address. So I see this book as a useful adjunct, but not the whole story, and I would say not the most important part. For example, it is not at all clear to me how the use of Pearl’s method would have voided the financial crisis.

      But maybe if I read on? Can anyone suggest a relevant quote?

      .

  2. Bayesian rules don´t lead anywhere. It´s a thought figure with no use in social sciences. It should be banned because it doesn´t lead anywhere for other than limited, technical reasons. Begone! Bayes!

    • It seems to me that people use Bayesian rules because they have been taught it and are not aware of any better alternatives. Can you point to any? (And what do you make of Pearl’s variations?)

      • You always at least have the frequentist approach Dave ,with all it´s limitations with focuses on P(D|H, not P(H|D), as Bayes, 🙂 !All the best!

      • But Dave,in many ways i think , C.Wright Mills words on methodology in social-sciences is still valid – Mills created tips to help conduct valid and reliable social-science studies, using the “sociological imagination”:

        “1.Be a good craftsman: Avoid any rigid set of procedures. Above all, seek to develop and to use the sociological imagination. Avoid the fetishism of method and technique. Urge the rehabilitation of the unpretentious intellectual craftsman, and try to become such a craftsman yourself. Let every man be his own methodologist; let every man be his own theorist; let theory and method again become part of the practice of a craft. Stand for the primacy of the individual scholar; stand opposed to the ascendancy of research teams of technicians. Be one mind that is on its own confronting the problems of man and society.

        2.Avoid the Byzantine oddity of associated and disassociated Concepts, the mannerism of verbiage. Urge upon yourself and upon others the simplicity of clear statement. Use more elaborated terms only when you believe firmly that their use enlarges the scope of your sensibilities, the precision of your references, the depth of your reasoning. Avoid using unintelligibility as a means of evading the making of judgments upon society—and as a means of escaping your readers’ judgments upon your own work.

        3.Make any trans-historical constructions you think your work requires; also delve into sub-historical minutiae. Make up quite formal theory and build models as well as you can. Examine in detail little facts and their relations, and big unique events as well. But do not be fanatic: relate all such work, continuously and closely, to the level of historical reality. Do not assume that somebody else will do this for you, sometime, somewhere. Take as your task the defining of this reality; formulate your problems in its terms; on its level try to solve these problems and thus resolve the issues and the troubles they incorporate. And never write more than three pages without at least having in mind a solid example.

        4.Do not study merely one small milieu after another; study the social structures in which milieux are organized. In terms of these studies of larger structures, select the milieux you need to study in detail, and study them in such a way as to understand the interplay of milieux with structure. Proceed in a similar way in so far as the span of time is concerned. Do not be merely a journalist, however a precise one. Know that journalism can be a great intellectual endeavor, but know also that yours is greater! So do not merely report minute researches into static knife-edge moments, or very short-term runs of time. Take as your time—span the course of human history, and locate within it the weeks, years, epochs you examine.

        5.Realize that your aim is a fully comparative understanding of the social structures that have appeared and that do now exist in world history. Realize that to carry it out you must avoid the arbitrary specialization of prevailing academic departments. Specialize your work variously, according to topic, and above all according to significant problem. In formulating and in trying to solve these problems, do not hesitate, indeed seek, continually and imaginatively, to draw upon the perspectives and materials, the ideas and methods, of any and all sensible studies of man and society. They are your studies; they are part of what you are a part of; do not let them be taken from you by those who would close them off by weird jargon and pretensions of expertise.

        6.Always keep your eyes open to the image of man—the generic notion of his human nature—which by your work you are assuming and implying; and also to the image of history—your notion of how history is being made. In a word, continually work out and revise your views of the problems of history, the problems of biography, and the problems of social structure in which biography and history intersect. Keep your eyes open to the varieties of individuality, and to the modes of epochal change. Use what you see and what you imagine, as the clues to your study of the human variety.

        7.Know that you inherit and are carrying on the tradition of classic social analysis; so try to understand man not as an isolated fragment, not as an intelligible field or system in and of itself. Try to understand men and women as historical and social actors, and the ways in which the variety of men and women are intricately selected and intricately formed by the variety of human societies. Before you are through with any piece of work, no matter how indirectly on occasion, orient it to the central and continuing task of understanding the structure and the drift, the shaping and the meanings, of your own period, the terrible and magnificent world of human society in the second half of the twentieth century.

        8.Do not allow public issues as they are officially formulated, or troubles as they are privately felt, to determine the problems that you take up for study. Above all, do not give up your moral and political autonomy by accepting in somebody else’s terms the illiberal practicality of the bureaucratic ethos or the liberal practicality of the moral scatter. Know that many personal troubles cannot be solved merely as troubles, but must be understood in terms of public issues—and in terms of the problems of history-making. Know that the human meaning of public issues must be revealed by relating them to personal troubles—and to the problems of the individual life. Know that the problems of social science, when adequately formulated, must include both troubles and issues, both biography and history, and the range of their intricate relations. Within that range the life of the individual and the making of societies occur; and within that range the sociological imagination has its chance to make a difference in the quality of human life in our time! ”

        C. Wright Mils, The Sociological Imagination,1959

        • Jan, Your Wright Mills quote seems much more insightful than a reference to frequentism. Does it link to any general theories of probability or knowledge, or does Wright Mills regard sociology as requiring a completely different kind of analysis and rationality from the hard sciences?

          • Dear Dave, here you have some about and from C.Wright Mills,all the best! http://garyrolfe.net/documents/cwrightmills.pdf
            https://www.imprs-demogr.mpg.de/courses/01ws/TSI.pdf

            • Thanks. The link to nursing and ‘evidence based practice’ seems of great importance outside of economics., and seems to me an example to show that Pearl is not addressing the whole problem.

              As a mathematician I accept that Whitehead et al are hard going. C. Wright Mill seems very accessible and not particularly obscure, so how come we are still in need of his wisdom?

              • Dave,infact Mills was pretty good on math himself,trained by his Professor Paul Lazarafeld,the mathematican that once worked with Albert Einstein but that turned in to sociology when he came to US and Columbia University.

                • Interesting. Mills is credited with founding mathematical sociology. But how is his understanding, as in your quote, reflected today?

                  I came across ‘Bayesian Affect Control Theory’ which, it seems to me, is consistent with the view that mainstream sociologists think that mathematics is nothing but computation. Moreover, it seems to me that simply replacing mainstream economic models of interaction with BACT would make economics more realistic, but they still wouldn’t be able to address financial crises adequately. So in so far as economics ought to take account of both mathematics and sociology, Mills seems to offer a lot more insight than contemporary mathematical sociology. Or am I mis-reading or missing something?


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