The development of Bayesian integration in sensorimotor estimation

Abstract

Examining development is important in addressing questions about whether Bayesian principles are hard coded in the brain. If the brain is inherently Bayesian, then behavior should show the signatures of Bayesian computation from an early stage in life. Children should integrate probabilistic information from prior and likelihood distributions to reach decisions and should be as statistically efficient as adults, when individual reliabilities are taken into account. To test this idea, we examined the integration of prior and likelihood information in a simple position-estimation task comparing children ages 6–11 years and adults. Some combination of prior and likelihood was present in the youngest sample tested (6–8 years old), and in most participants a Bayesian model fit the data better than simple baseline models. However, younger subjects tended to have parameters further from the optimal values, and all groups showed considerable biases. Our findings support some level of Bayesian integration in all age groups, with evidence that children use probabilistic quantities less efficiently than adults do during sensorimotor estimation.

An Adaptive Cue Selection Model of Allocentric Spatial Reorientation

“…Adaptive Selection is a non-Bayesian process of selecting the best single cue and using it in isolation. For children under 10 years, this is in line with previous research regarding the use of multiple cues (Adams, 2016;Chambers et al, 2018;Dekker et al, 2015;Gori et al, 2012;Jovanovic & Drewing, 2014;Nardini et al, 2010Nardini et al, , 2013Nardini et al, , 2008Petrini et al, 2014). Re-analysis of previous data agrees as well.…”

“…If Adaptive Combination is true, it is also a breakthrough finding for the study of developing Bayes-like reasoning in perception and memory. Almost all previous studies to look at Bayesian cue combination in children under 10 years old have returned negative results (Adams, 2016;Chambers, Sokhey, Gaebler-Spira, & Kording, 2018;Dekker et al, 2015;Gori, Sandini, & Burr, 2012;Jovanovic & Drewing, 2014;Nardini, Bedford, & Mareschal, 2010;Nardini, Begus, & Mareschal, 2013;Petrini, Remark, Smith, & Nardini, 2014), including one that looked at combination of cues for spatial recall (Nardini, Jones, Bedford, & Braddick, 2008). For example, when judging a horizontal location with a spatialized audio cue and a brief visual cue, children under 10 years old fail to integrate the two efficiently; the precision of their judgements is not any better than with the visual cue alone .…”

Young children combine sensory cues with learned information in a statistically efficient manner: But task complexity matters

“…Our findings suggest an alternative interpretation: rather than being incapable of Bayes-optimal computations, young children might have responded to the complexity of their task by reverting to a computationally simpler but sub-optimal strategy, with task complexity affecting young children's behavior to a greater extent than that of adults. Indeed, the Chambers et al (2018) study involved a task with an intermediate level of complexity (compared to the two experiments in our study), so it is interesting to note that 6-to 8-yearolds demonstrated a pattern of behavior that was intermediate in sophistication (consistent with predictions of Model 2 described above), compared to that observed in the two experiments in our study.…”

“…Our findings have important implications for how we should interpret failures in young children's ability to carry out sophisticated computations. For instance, in a recent study, Chambers et al (2018) used a similar spatial localization task to examine the extent to which 6-11-year-olds and adults combined uncertain sensory information with prior information. Notably, targets were drawn from one of two underlying Gaussian distributions in a blocked fashion (via four alternating blocks of 120 trials), and they did not examine learning (a cue to the block-relevant prior was always visible on the screen).…”

“…Recently, some studies have reported that young children differ substantially from adults in their ability to mitigate the influence of sensory uncertainty by utilizing multiple sources of information (Barutchu, Crewther, & Crewther, 2008;Chambers, Sokhey, Gaebler-Spira, & Kording, 2018;Gori, Del Viva, Sandini, & Burr, 2008;Nardini, Bedford, & Mareschal, 2010;Nardini, Jones, Bedford, & Braddick, 2008;Petrini, Remark, Smith, & Nardini, 2014). For instance, several studies have shown that when presented with multiple simultaneous cues children younger than 8-12 years of age combine these cues in a suboptimal manner -their behavior is often dominated by one of the cues irrespective of its relative reliability.…”