In his preface to Copernicus's masterpiece, Osiander wrote, “For these hypotheses need not be true or even probable; if they provide a calculus consistent with the observations, that alone is sufficient” (Copernicus Reference Copernicus1995).
So far as I can tell, Bayesian psychologists are doing the kind of thing Osiander said astronomers should be doing. Bayesian psychologists collect data from experiments and in each case provide a model for the data. In these models, subjects have prior probabilities for various hypotheses and likelihoods for the data on each hypothesis. Stimuli change their degrees of belief according to Bayes’ Rule, and then the experimental subjects somehow use the updated probabilities to perform some action. The minimal Bayesian psychological claim is just that various experiments on learning behavior can be accommodated in this way. That also seems to be the maximal claim. Bayesian psychologists – at least those I read and talk with – do not claim that their subjects are deliberately, consciously, carrying out a computation of posterior degrees of belief, and deliberately, consciously, using the result in a decision rule. In many cases that would be implausible, and in any case, if that were the claim, a bit of protocol elicitation would confirm or disconfirm it. But neither do Bayesian psychologists exactly say that their participants are carrying out the Bayesian computations and applying the decision rule unconsciously.
That some Bayesian model or other succeeds in accommodating learning data is no surprise: The experimenters get to screen the subjects, to postulate the priors, and to postulate post hoc the rules – however irrational they may appear by decision theoretical standards – mapping posterior probabilities to behavior. Caution and modesty are virtues in science and in life, and agnosticism may be the best theology, but vacuity is not a scientific virtue. Here is a list of further complaints:
First, for a computationally bounded agent, there is neither a theoretical nor a practical rationale for learning and judgment exclusively in accord with Bayesian principles.
Second, the Bayesian framework itself is empirically vacuous: Anything, or almost anything, could be explained by adjusting priors and likelihoods.
Third, experiments showing “probability matching” in forced choice learning tasks are prima facie in conflict with Bayesian criteria for rationality. Bayesian explanations require an ad hoc error theory that is seldom, if ever, justified empirically.
Fourth, scientific practice shows that Bayesian principles are inadequate when novel hypotheses are introduced to explain previously accepted data. Old evidence, long established, is taken to be evidence for novel hypotheses. (The most famous example: The anomalous advance of the perihelion of Mercury, established in 1858, was evidence for the novel general theory of relativity, announced in 1915.) Similar behavior should be expected in psychological experiments, although I don’t know of any test of this expectation. By Bayesian principles, established evidence, fully believed, cannot confirm or support novel hypotheses.
Fifth, these points, as well as many of Jones & Love's (J&L's) in the target article, have already been made in the philosophical literature (Eberhardt & Danks, in press; Glymour Reference Glymour, Harper and Wheeler2007), which Bayesian advocates have largely ignored. As J&L suggest in their title, some Bayesian cognitive modelers do seem to be fundamentalists.
What could be the point of all this ritualistic mathematical modeling? Ptolemy, for all of the infinite flexibility of his modeling devices, at least predicted future eclipses and positions of the planets, the sun, and the moon. I know of no Bayesian psychological prediction more precise than “We can model it.” Ptolemy at least found robust regularities of the observed variables. I know of no essentially Bayesian psychological discovery of a robust behavioral regularity – that is of a prediction of a phenomenon that would not be expected on contrary grounds. Sometimes the Bayesian claim is that a Bayesian model saves the phenomena better than specific alternatives do, but that depends on the phenomena and the alternatives. Since Bayesian models came into fashion, psychological hands are sometimes waved toward Bayesian accounts when simple heuristics would account for the subjects’ judgments as well or better.
J&L propose bigamous weddings, one of Bayesian psychology to the rest of conventional cognitive psychology, and one of Bayesian psychology to cognitive neuropsychology. The latter pairing may prosper, but I strongly suspect it will be a marriage of unequal partners: The neuropsychologists will be the breadwinners. In any case, the interesting recent and current work on neural encodings that can be interpreted to represent probabilities and conditional probabilities is at an astronomical distance from Bayesian psychological models.
At least Bayesian psychology at least does no harm. It does not obfuscate like psychoanalysis, Hegelian metaphysics, or postmodern literary studies. Its real cost is in the lost opportunities for good minds to advance our understanding of how the brain produces thought, emotion, and action.
In his preface to Copernicus's masterpiece, Osiander wrote, “For these hypotheses need not be true or even probable; if they provide a calculus consistent with the observations, that alone is sufficient” (Copernicus Reference Copernicus1995).
So far as I can tell, Bayesian psychologists are doing the kind of thing Osiander said astronomers should be doing. Bayesian psychologists collect data from experiments and in each case provide a model for the data. In these models, subjects have prior probabilities for various hypotheses and likelihoods for the data on each hypothesis. Stimuli change their degrees of belief according to Bayes’ Rule, and then the experimental subjects somehow use the updated probabilities to perform some action. The minimal Bayesian psychological claim is just that various experiments on learning behavior can be accommodated in this way. That also seems to be the maximal claim. Bayesian psychologists – at least those I read and talk with – do not claim that their subjects are deliberately, consciously, carrying out a computation of posterior degrees of belief, and deliberately, consciously, using the result in a decision rule. In many cases that would be implausible, and in any case, if that were the claim, a bit of protocol elicitation would confirm or disconfirm it. But neither do Bayesian psychologists exactly say that their participants are carrying out the Bayesian computations and applying the decision rule unconsciously.
That some Bayesian model or other succeeds in accommodating learning data is no surprise: The experimenters get to screen the subjects, to postulate the priors, and to postulate post hoc the rules – however irrational they may appear by decision theoretical standards – mapping posterior probabilities to behavior. Caution and modesty are virtues in science and in life, and agnosticism may be the best theology, but vacuity is not a scientific virtue. Here is a list of further complaints:
First, for a computationally bounded agent, there is neither a theoretical nor a practical rationale for learning and judgment exclusively in accord with Bayesian principles.
Second, the Bayesian framework itself is empirically vacuous: Anything, or almost anything, could be explained by adjusting priors and likelihoods.
Third, experiments showing “probability matching” in forced choice learning tasks are prima facie in conflict with Bayesian criteria for rationality. Bayesian explanations require an ad hoc error theory that is seldom, if ever, justified empirically.
Fourth, scientific practice shows that Bayesian principles are inadequate when novel hypotheses are introduced to explain previously accepted data. Old evidence, long established, is taken to be evidence for novel hypotheses. (The most famous example: The anomalous advance of the perihelion of Mercury, established in 1858, was evidence for the novel general theory of relativity, announced in 1915.) Similar behavior should be expected in psychological experiments, although I don’t know of any test of this expectation. By Bayesian principles, established evidence, fully believed, cannot confirm or support novel hypotheses.
Fifth, these points, as well as many of Jones & Love's (J&L's) in the target article, have already been made in the philosophical literature (Eberhardt & Danks, in press; Glymour Reference Glymour, Harper and Wheeler2007), which Bayesian advocates have largely ignored. As J&L suggest in their title, some Bayesian cognitive modelers do seem to be fundamentalists.
What could be the point of all this ritualistic mathematical modeling? Ptolemy, for all of the infinite flexibility of his modeling devices, at least predicted future eclipses and positions of the planets, the sun, and the moon. I know of no Bayesian psychological prediction more precise than “We can model it.” Ptolemy at least found robust regularities of the observed variables. I know of no essentially Bayesian psychological discovery of a robust behavioral regularity – that is of a prediction of a phenomenon that would not be expected on contrary grounds. Sometimes the Bayesian claim is that a Bayesian model saves the phenomena better than specific alternatives do, but that depends on the phenomena and the alternatives. Since Bayesian models came into fashion, psychological hands are sometimes waved toward Bayesian accounts when simple heuristics would account for the subjects’ judgments as well or better.
J&L propose bigamous weddings, one of Bayesian psychology to the rest of conventional cognitive psychology, and one of Bayesian psychology to cognitive neuropsychology. The latter pairing may prosper, but I strongly suspect it will be a marriage of unequal partners: The neuropsychologists will be the breadwinners. In any case, the interesting recent and current work on neural encodings that can be interpreted to represent probabilities and conditional probabilities is at an astronomical distance from Bayesian psychological models.
At least Bayesian psychology at least does no harm. It does not obfuscate like psychoanalysis, Hegelian metaphysics, or postmodern literary studies. Its real cost is in the lost opportunities for good minds to advance our understanding of how the brain produces thought, emotion, and action.