Spatial attention, precision, and Bayesian inference: a study of saccadic response speed

Abstract

Inferring the environment's statistical structure and adapting behavior accordingly is a fundamental modus operandi of the brain. A simple form of this faculty based on spatial attentional orienting can be studied with Posner's location-cueing paradigm in which a cue indicates the target location with a known probability. The present study focuses on a more complex version of this task, where probabilistic context (percentage of cue validity) changes unpredictably over time, thereby creating a volatile environment. Saccadic response speed (RS) was recorded in 15 subjects and used to estimate subject-specific parameters of a Bayesian learning scheme modeling the subjects' trial-by-trial updates of beliefs. Different response models-specifying how computational states translate into observable behavior-were compared using Bayesian model selection. Saccadic RS was most plausibly explained as a function of the precision of the belief about the causes of sensory input. This finding is in accordance with current Bayesian theories of brain function, and specifically with the proposal that spatial attention is mediated by a precision-dependent gain modulation of sensory input. Our results provide empirical support for precision-dependent changes in beliefs about saccade target locations and motivate future neuroimaging and neuropharmacological studies of how Bayesian inference may determine spatial attention.

Keywords: cue validity; hierarchical models; variational Bayes; visuospatial processing; volatility.

Figure 1.

Illustration of the experimental task and the manipulation of %CV over the 612 trials.

Figure 2.

Graphical illustration of the perceptual (generative) model with states x₁, x₂, and x₃. The model parameters ω and impact on the time course of subjects' inferred belief about the states x and are estimated from the individual subject RS data. Circles represent constants, while diamonds represent quantities that change in time (i.e., that carry a time (or trial) index). Hexagons, like diamonds, represent quantities that change in time but that additionally depend on their previous state in time in a Markovian fashion.

Figure 3.

Illustration of the relationship between RS (inverse RT) and the quantity , representing the amount of attentional resources allocated to the cued location. For each response model, RS were assumed to be linearly related to (which differs between the 3 models, see Appendix). Note the opposite behaviour of RS for increasing on valid (black line and equation) and invalid (gray line and equation) trials (cf. eq. 5).

Figure 4.

Illustration of the amount of attentional resources for the 3 different theoretical response models as a function of .

Figure 5.

(A) Average RS in valid and invalid trials for the 3 (true) %CV levels. Error bars depict standard errors of the mean (SEM) (B) Illustration of how the observed RS costs after invalid cueing translate into RT differences (in ms).

Figure 6.

(A) Illustration of the subject-specific patterns for the values of the volatility estimate ω and the meta-volatility estimate . (B) Illustration of minimal and maximal RS (as derived from the response model parameters ζ₁ (averaged for valid and invalid trials) and ζ₂) in relation to overall (mean) RS. The symbols single and double asterisks denote the data from subjects A and B depicted in Figure 8, respectively.

Figure 7.

Relationship between the perceptual parameters ω and , and the Rescorla–Wagner learning rate ε.

Figure 8.

Illustration of the time course of μ₃ (upper panels) and s(μ₂) (lower panels) during observation of x₁ (black diamonds) for 2 exemplary subjects with different parameters for ω and . The true %CV is depicted as a dotted line. It can be seen that subject A (ω = −6.09; ) shows slower updating of the probability estimate that the target will appear at the cued location than subject B (ω = −2.78; ). This can be attributed to subject A's lower value of ω (reflecting the subject's belief in a less volatile environment).

Figure 9.

(A) Observed and predicted average RS in valid and invalid trials as a function of the precision-dependent attentional weight parameter (attention to cued location; calculated for the group average values). Error bars depict standard errors of the mean (SEM). The lines correspond to the predictions using the average response model parameters, over subjects. (B) Illustration of how the observed RS costs after invalid cueing translate into RT differences (in ms).