Abstract
Colombo and Hartmann (Br J Philos Sci 68(2):451–484. https://doi.org/10.1093/bjps/axv036, 2017) recently argued that Bayesian modelling in neuroscience can not only unify a diverse range of behavioral phenomena under a common mathematical framework, but can also place useful constraints on both mechanism discovery and confirmation among competing mechanistic models. After reviewing some reasons for decoupling unification and explanation, we raise two challenges for their view. First, although they attempt to distance themselves from the view that Bayesian models provide mechanistic explanations, to the extent that a given model successfully constrains the search space for possible mechanisms, it will convey at least some mechanistic information and therefore automatically qualify as a partial or incomplete mechanistic explanation. Second, according to their view, one widely used strategy to guide and constrain mechanism discovery involves assuming a mapping between features of a behaviorally confirmed Bayesian model and features of the neural mechanisms underlying the behavior. Using their own example of multisensory integration, we discuss how competing mechanistic models can be consistent with all available behavioral data and yet be inconsistent with each other. This tension reveals that there are exploitable degrees of freedom in the mapping relationship between models of behavioral phenomena and neural mechanisms, and points to the role that other background assumptions play including level-assumptions about the appropriate level at which the neural model should be specified (e.g., individual neuron or population level) and localization-assumptions about where in the system the underlying mechanism might occur. These considerations highlight the need for a more refined account of modelling constraints in neuroscience.
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Notes
- 1.
Although we explore these issues in the context of Bayesian models of behavior, these considerations likely have more general applicability.
- 2.
It should be noted that although some accounts may be more difficult to locate in terms of this binary distinction than others, our primary aim is to characterise two broad trends in the scientific literature. We do not assume that all accounts will be neatly accommodated by this distinction. For example, views that claim that probabilistic models operate at the “computational level”, in Marr’s sense, are difficult to place cleanly on one side of this distinction or the other because Marr’s notion is itself subject to various competing interpretations (Shagrir and Bechtel 2017). Taking a stance on this debate goes well beyond the scope of the current chapter.
- 3.
It is only nearly as bad an inference because at least in this case we have independent reasons to believe the target system is computational. Thanks to Matteo Colombo for pointing this out.
- 4.
Although we are aware of the general tension between frequentist and epistemic conceptions of probability and the related debate about how to interpret priors in probabilistic models (see Feldman 2013), the interpretation of the prior in this experiment seems relatively straightforward. Because the prior distribution each subject experienced was set empirically and was the product of a random (or pseudo-random) process — each experienced shift was drawn randomly (pseudo-randomly) from a Gaussian distribution — it seems to us that the prior probabilities can be interpreted as physical probabilities and a frequentist conception is appropriate. We thank Brendan Ritchie for bringing this point to our attention.
- 5.
As another high-profile example, Ernst and Banks (2002) draw a similar conclusion about the nervous system performing Bayesian integration on the basis of behavioral performance in a cue combination task. They state: “we found that height judgements were remarkably similar to those predicted by the MLE integrator. Thus, the nervous system seems to combine visual and haptic information in fashion similar to the MLE rule.” (2002, 431)
- 6.
The notion of coherence is a technical one from formal epistemology. For details, see the mathematical proof supplied by Colombo and Hartmann (2017).
- 7.
Colombo and Hartmann (2017) cite some of these and many others.
- 8.
- 9.
Scope concerns how many systems or how many different kinds of systems there actually are to which a given model or generalization applies, and so is highly similar to (or at least strongly correlated with) unifying power.
- 10.
This does not entail the drive towards something like exhaustive model completeness for which the goal is that all details, relevant and irrelevant, are included. For details, see Craver and Kaplan (2018).
- 11.
It is worth noting that this characterization of model scope might elide a further distinction between the ways in which scope can vary. For example, scope can refer to the same type of mechanism for the same type of phenomenon that is instantiated by many systems across different taxa. Alternatively, scope can refer to the same type of mechanism for many different types of phenomena that is instantiated by many systems across different species/taxa. Although these are importantly different, we would argue that wide scope in either of these senses is not required for a given model to explain. We thank Matteo Colombo for bringing this distinction to our attention.
- 12.
There are some important parallels between the view we advocate in this chapter and the account developed by Zednik and Jäkel (2016). In that work, they offer an account of “Bayesian reverse engineering” according to which arriving at an explanatorily adequate model involves an ordered and iterative search through three different “hypothesis spaces” each of which is associated with one of Marr’s levels — the computational, algorithmic, and implementational. Although there are a number of similarities between our view and theirs, there are also important differences, including different starting points: Marrian levels versus mechanistic explanations. It is, however, beyond the scope of this chapter to explore these similarities and differences and remains work for another day (for related discussion, See Bechtel and Shagrir (2015)).
- 13.
Zednik and Jäkel (2016) use the term ‘push-down heuristic’ to describe something very similar.
- 14.
The details here are complex but the basic idea is that MSTd neurons exhibit lower firing rates for high coherence visual stimuli presented in the null (anti-preferred) direction than for low coherence in the null direction. This means that MSTd neuron responses are nonlinear (i.e., not multiplicative) at the flanks of their tuning curves, which violates the assumptions of the PPC model. This topic remains an active area of investigation (Fetsch, personal communication).
- 15.
Zednik and Jäkel (2016) introduce the useful term ‘tweak’ to characterize a similar practice in Bayesian ideal observer modelling of behavioral data.” They maintain that tweaks reflect the available “degrees of freedom that researchers may exploit to accommodate the observed behavioral data” (Zednik and Jäkel 2016, 3959). We would argue for expanding the notion of tweaking to cover modelling practices at the neural- or implementational-level. Here we have identified several examples of this kind of model tweaking.
- 16.
In mathematics, a monotonic function is either entirely nonincreasing or nondecreasing. A function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function that decreases monotonically does not exclusively have to decrease, it simply must not increase.
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Acknowledgements
We would like to thank Krys Dolega, Colin Klein, Oron Shagrir, Alessio Plebe, Carlos Zednik, and especially Matteo Colombo and Brendan Ritchie for their insightful feedback.
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Kaplan, D.M., Hewitson, C.L. (2021). Modelling Bayesian Computation in the Brain: Unification, Explanation, and Constraints. In: Calzavarini, F., Viola, M. (eds) Neural Mechanisms. Studies in Brain and Mind, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-030-54092-0_2
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