Bayesian Statistics seminars

In the current virtual journal club Dr Di Luca will present findings from a series of psychophysical investigations where he measured sensitivity and bias in the perception of the timing of stimuli. He will present how improved detection with longer sequences and biases in reporting isochrony can be accounted for by optimal statistical predictions. Among his findings was also that the timing of stimuli that occasionally deviate from a regularly paced sequence is perceptually distorted to appear more regular. Such change depends on whether the context these sequences are presented is also regular. Dr Di Luca will present a Bayesian model for the combination of dynamically updated expectations, in the form of a priori probability, with incoming sensory information. These findings contribute to the understanding of how the brain processes temporal information to shape perceptual experiences.

Psychology and neuroscience are increasingly looking to fine-grained analyses of decision-making behaviour, seeking to characterise not just the variation between subjects but also a subject's variability across time. When analysing the behaviour of each subject in a choice task, we ideally want to know not only when the subject has learnt the correct choice rule but also what the subject tried while learning. I introduce a simple but effective Bayesian approach to inferring the probability of different choice strategies at trial resolution. This can be used both for inferring when subjects learn, by tracking the probability of the strategy matching the target rule, and for inferring subjects use of exploratory strategies during learning. Applied to data from rodent and human decision tasks, we find learning occurs earlier and more often than estimated using classical approaches. Around both learning and changes in the rewarded rules the exploratory strategies of win-stay and lose-shift, often considered complementary, are consistently used independently. Indeed, we find the use of lose-shift is strong evidence that animals have latently learnt the salient features of a new rewarded rule. Our approach can be extended to any discrete choice strategy, and its low computational cost is ideally suited for real-time analysis and closed-loop control.

Mobile organisms must be capable of deciding both where and when to move in order to keep up with a changing environment; therefore, a strong sense of time is necessary, otherwise, we would fail in many of our movement goals. Despite this intrinsic link between movement and timing, only recently has research begun to investigate the interaction. Two primary effects that have been observed include: movements biasing time estimates (i.e., affecting accuracy) as well as making time estimates more precise. The goal of this presentation is to review this literature, discuss a Bayesian cue combination framework to explain these effects, and discuss the experiments I have conducted to test the framework. The experiments herein include: a motor timing task comparing the effects of movement vs non-movement with and without feedback (Exp. 1A & 1B), a transcranial magnetic stimulation (TMS) study on the role of the supplementary motor area (SMA) in transforming temporal information (Exp. 2), and a perceptual timing task investigating the effect of noisy movement on time perception with both visual and auditory modalities (Exp. 3A & 3B). Together, the results of these studies support the Bayesian cue combination framework, in that: movement improves the precision of time perception not only in perceptual timing tasks but also motor timing tasks (Exp. 1A & 1B), stimulating the SMA appears to disrupt the transformation of temporal information (Exp. 2), and when movement becomes unreliable or noisy there is no longer an improvement in precision of time perception (Exp. 3A & 3B). Although there is support for the proposed framework, more studies (i.e., fMRI, TMS, EEG, etc.) need to be conducted in order to better understand where and how this may be instantiated in the brain; however, this work provides a starting point to better understanding the intrinsic connection between time and movement

Solutions to challenging inference problems are often subject to a fundamental trade-off between bias (being systematically wrong) that is minimized with complex inference strategies and variance (being oversensitive to uncertain observations) that is minimized with simple inference strategies. However, this trade-off is based on the assumption that the strategies being considered are optimal for their given complexity and thus has unclear relevance to the frequently suboptimal inference strategies used by humans. We examined inference problems involving rare, asymmetrically available evidence, which a large population of human subjects solved using a diverse set of strategies that were suboptimal relative to the Bayesian ideal observer. These suboptimal strategies reflected an inversion of the classic bias-variance trade-off: subjects who used more complex, but imperfect, Bayesian-like strategies tended to have lower variance but high bias because of incorrect tuning to latent task features, whereas subjects who used simpler heuristic strategies tended to have higher variance because they operated more directly on the observed samples but displayed weaker, near-normative bias. Our results yield new insights into the principles that govern individual differences in behavior that depends on rare-event inference, and, more generally, about the information-processing trade-offs that are sensitive to not just the complexity, but also the optimality of the inference process.

Hongjing Lu will present a new computational model of Probabilistic Analogical Mapping (PAM, in collaboration with Nick Ichien and Keith Holyoak) that finds systematic correspondences between inputs generated by machine learning. The model adopts a Bayesian framework for probabilistic graph matching, operating on semantic relation networks constructed from distributed representations of individual concepts (word embeddings created by Word2vec) and of relations between concepts (created by our BART model). We have used PAM to simulate a broad range of phenomena involving analogical mapping by both adults and children. Our approach demonstrates that human-like analogical mapping can emerge from comparison mechanisms applied to rich semantic representations of individual concepts and relations. More details can be found https://arxiv.org/ftp/arxiv/papers/2103/2103.16704.pdf

Interval timing is a fundamental component action, and is susceptible to motor-related temporal distortions. Previous studies have shown that movement biases temporal estimates, but have primarily considered self-modulated movement only. However, real-world encounters often include situations in which movement is restricted or perturbed by environmental factors. In the following experiments, we introduced viscous movement environments to externally modulate movement and investigated the resulting effects on temporal perception. In two separate tasks, participants timed auditory intervals while moving a robotic arm that randomly applied four levels of viscosity. Results demonstrated that higher viscosity led to shorter perceived durations. Using a drift-diffusion model and a Bayesian observer model, we confirmed these biasing effects arose from perceptual mechanisms, instead of biases in decision making. These findings suggest that environmental perturbations are an important factor in movement-related temporal distortions, and enhance the current understanding of the interactions of motor activity and cognitive processes. https://www.biorxiv.org/content/10.1101/2020.10.26.355396v1