Bayesian comparison of explicit and implicit causal inference strategies in multisensory heading perception

Abstract

The precision of multisensory perception improves when cues arising from the same cause are integrated, such as visual and vestibular heading cues for an observer moving through a stationary environment. In order to determine how the cues should be processed, the brain must infer the causal relationship underlying the multisensory cues. In heading perception, however, it is unclear whether observers follow the Bayesian strategy, a simpler non-Bayesian heuristic, or even perform causal inference at all. We developed an efficient and robust computational framework to perform Bayesian model comparison of causal inference strategies, which incorporates a number of alternative assumptions about the observers. With this framework, we investigated whether human observers’ performance in an explicit cause attribution and an implicit heading discrimination task can be modeled as a causal inference process. In the explicit causal inference task, all subjects accounted for cue disparity when reporting judgments of common cause, although not necessarily all in a Bayesian fashion. By contrast, but in agreement with previous findings, data from the heading discrimination task only could not rule out that several of the same observers were adopting a forced-fusion strategy, whereby cues are integrated regardless of disparity. Only when we combined evidence from both tasks we were able to rule out forced-fusion in the heading discrimination task. Crucially, findings were robust across a number of variants of models and analyses. Our results demonstrate that our proposed computational framework allows researchers to ask complex questions within a rigorous Bayesian framework that accounts for parameter and model uncertainty.

Human online adaptation to changes in prior probability

“…(1) It is important to test alternatives to Bayesian models: observers’ behavior might be explained without requiring an internal representation of probability. (2) Using multiple tasks together with rigorous model comparison can provide additional insight into behavior (see also [38]). Here, the fluctuations in decision criteria between change points led to suboptimal behavior.…”

Explaining the effects of distractor statistics in visual search

“…The set with the highest likelihood was used as the start point for the run. The bounds on the parameters during the search, and the way in which initial parameter values were drawn, is described in appendix E. Running the fitting procedure many times reduces the chance of getting stuck in local maxima, and permits heuristic assessment of any problems local maxima may be causing (see supplementary methods of Acerbi, Dokka, Angelaki & Ma, 2018). We found that fits to the same log-likelihood function often ended at different values of "maximum" log-likelihood, suggesting that we may have only found local maxima, rather than finding the global maximum.…”

“…For each model and participant, we performed maximum-likelihood fitting 40 times. Fitting 40 times allowed us to estimate the probability that our best fits were reaching the true maximum-likelihood, as oppose to getting stuck in local maxima (see supplementary methods of Acerbi et al, 2018). To do this, we looked at how many fits ended up close to the best value of the likelihood found.…”

Causal inference for spatial constancy across whole body motion

“…Previous research has reported similar intersubject variability in saccadic updating (Atsma et al 2016). It remains unclear whether this parameter provides an actual readout of the participant's prior belief about a common cause: Recent research has shown that the estimated p(C ϭ 1) did not always match the experimental p(C ϭ 1) (Acerbi et al 2018). Across subjects, our results suggest that updating responses rely on a Bayesian causal inference.…”

“…In this study and in previous work (Atsma et al 2016) we assumed that the computations regarding causal inference for spatial constancy are Bayes optimal, and thus the decision boundary for the presence of a common cause is uncertainty dependent. A more recent study (Acerbi et al 2018) suggested a decision rule solely depending on the observed spatial difference between the cues and some fixed criterion. Future work would need to explicitly manipulate uncertainty and test both cues independently (e.g., report the location of the probe and the visual target independently) in order to compare these decision rules.…”