Bayesian Practice and the Persistence of Inductive Risk

Current abstract

Bayesian replies to the argument from inductive risk often begin from Richard Jeffrey’s thought that scientists need not accept/reject hypotheses; they can assign probabilities. Recent defenses extend this, suggesting that Bayesianism can avoid at least the main force of the argument. I argue that once Bayesianism is treated as actual statistical practice, rather than an idealized theory of graded belief, familiar forms of methodological underdetermination reappear. Choices about ambiguous data, priors/hyperpriors, computational diagnostics, and model comparison can all predictably shape posterior claims. In short, inductive risk arises in Bayesianism just as in frequentist statistics, albeit in different ways.

Accessible overview

Scientific conclusions can have consequences even when the evidence is uncertain. Philosophers describe the resulting problem as inductive risk: methodological choices can change the balance between possible errors, and those errors can have foreseeable consequences beyond science itself.

Richard Jeffrey’s influential reply held that scientists can assign probabilities rather than accept or reject hypotheses, leaving practical decisions to others. This paper argues that the reply identifies a real advantage of Bayesian inference but does not scale into a general escape from inductive risk. Once Bayesianism is understood as statistical practice—not only as an idealized theory of graded belief—methodological underdetermination reappears.

Where judgment persists

The argument follows four recurring sites of applied Bayesian judgment:

Ambiguous data. Latent-variable and measurement-error models can preserve uncertainty that a hard classification would erase, but analysts must still decide how that ambiguity is represented.
Priors and hyperpriors. Several specifications can be scientifically reasonable while producing meaningfully different posterior summaries, especially when evidence is sparse or decisions are urgent.
Computation and diagnostics. Approximate posterior computation requires judgments about convergence, effective information, and whether uncertainty—particularly in the tails—has been characterized well enough.
Model comparison and model space. Model averaging can propagate uncertainty across considered models, but it cannot determine whether the right alternatives and background assumptions entered the comparison in the first place.

Not every discretionary choice qualifies as a locus of inductive risk. The paper’s narrower claim concerns choices that are not settled by the evidence alone, can predictably shape the inference, and carry reasonably foreseeable consequences if the analysis is wrong.

A constructive conclusion

The conclusion is comparative rather than anti-Bayesian. Bayesian methods can make uncertainty easier to preserve, propagate, and inspect than threshold-centered alternatives. Their philosophical value may lie precisely in making the remaining sites of judgment visible—not in making those judgments disappear.

The paper is forthcoming in Philosophy of Science, with the final version expected in early 2027 following its presentation as a contributed paper at the Philosophy of Science Association meeting. No draft is linked while the working-paper version remains in development; a publication link will be added when the final version is available.