Likelihoodists admit that their methods provide no immediate guidance for belief or action. They nevertheless maintain that those methods are useful alternatives to Bayesian and frequentist approach to statistics (see e.g. Royall 1997, Ch. 1). I argue against various attempts to make this curious claim seem plausible in my paper “Why I Am Not a Likelihoodist.” There is one possible defense of this claim that the current draft of that paper does not address, namely that science itself is about evidential support rather than belief or action.2 This view is attractive even from a non-likelihoodist perspective because it makes the aims of science achievable. However, it does so at too high a cost by calling into question the value of achieving those aims, thereby calling into question the value of science itself.
The view that science is about evidential support rather than belief or action makes science safe against skeptical arguments such as brain-in-a-vat thought experiments and Hume’s problem of induction. It could be the case that our evidence favors Einstein’s theory of gravity over Newton’s, for instance, even if we are brains in vats who have no justification for believing that the laws of physics will be the same tomorrow as they are today. Similarly, because data can favor one false hypothesis over another, this view provides a possible account of what scientists are doing when they perform inference in the context of models that they know are false. Unlike frequentists and Bayesians, likelihoodists (qua likelihoodists) can make no errors provided that they perform their calculations correctly (Royall 2000, 761). The outputs of their methods are explicative claims about relationships between data and hypotheses, rather than contingent claims about relationships between theory and reality or between means and ends.
I take it that providing guidance for belief or action is more desirable than merely characterizing data as evidence, and thus that the claim that science is about evidential support only is attractive only on the view that it cannot provide such guidance. This view comes in a mild form and a radical form. In its mild form, it is just a claim about where science ends and its applications begin. According to this claim, science itself only has the resources to justify claims about evidential favoring. Resources adequate to justify claims about what we ought to believe or do are available to us, but they lie outside the scope of science, perhaps because they include subjective elements such as personal degrees of belief. In its radical form, by contrast, this view asserts that we lack the resources to justify claims about what we ought to believe or do full stop, rather than merely qua scientists.
In its mild form, the view that science cannot properly provide guidance for belief or action merely restricts the scope of science in a way that is either misguided or merely semantic. It is misguided if it implies that scientists should never attempt to provide guidance for belief and action in scientific fora such as scientific journals or conferences. It is merely semantic if it allows for this kind of activity and merely insists on refraining from labeling it “scientific.”
In its radical form, the view that science cannot properly provide guidance for belief or action gives us something we can say that we might regard as true even under various skeptical scenarios, but statements that are so secure against being mistaken cannot have much if any real content. We should not dismiss the possibility that the justification for claims about the evidential meaning of data is all that we can have. But that possibility provides a kind of vindication for likelihoodism at the expense of calling into question the value of doing science. If statements about evidential support are not enough to tell us what to believe or do, then they have no apparent value regardless of their truth or falsity.
In either form, the view that science cannot properly provide guidance for belief or action warrants the claim that likelihoodism is the appropriate epistemology for science at the expense of making science itself toothless. It takes the Pyrrhic approach of sacrificing science to save likelihoodism. It does not address the fact that likelihoodist methods, unlike Bayesian and frequentist methods, do not allow us to use likelihood functions to do any real work.
Royall, Richard. Statistical Evidence: A Likelihood Paradigm. Chapman & Hall/CRC, 1997.
Royall, Richard. “On the probability of observing misleading statistical evidence.” Journal of the American Statistical Association 95.451 (2000): 760-768.
- Photo taken with permission from Jan Kunst’s flickr page.
- Thanks to Edouard Machery for suggesting this response on behalf of likelihoodism.
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