Problems in estimating the response functions of natural climatic recording systems [abstract]

EXTRACT (SEE PDF FOR FULL ABSTRACT): High-resolution proxy records of climate, such as varves, ice cores, and tree-rings, provide the opportunity for reconstructing climate on a year-by-year basis. In order to do so it is necessary to approximate the complex nonlinear response function of the natural recording system using linear statistical models. Three problems with this approach were discussed, and possible solutions were suggested. Examples were given from a reconstruction of Santa Barbara precipitation based on tree-ring records from Santa Barbara County.

Near optimal combination of sensory and motor uncertainty in time during a naturalistic perception-action task.

Most behavioral tasks have time constraints for successful completion, such as catching a ball in flight. Many of these tasks require trading off the time allocated to perception and action, especially when only one of the two is possible at any time. In general, the longer we perceive, the smaller the uncertainty in perceptual estimates. However, a longer perception phase leaves less time for action, which results in less precise movements. Here we examine subjects catching a virtual ball. Critically, as soon as subjects began to move, the ball became invisible. We study how subjects trade-off sensory and movement uncertainty by deciding when to initiate their actions. We formulate this task in a probabilistic framework and show that subjects' decisions when to start moving are statistically near optimal given their individual sensory and motor uncertainties. Moreover, we accurately predict individual subject's task performance. Thus we show that subjects in a natural task are quantitatively aware of how sensory and motor variability depend on time and act so as to minimize overall task variability.

Representations of uncertainty in sensorimotor control.

Uncertainty is ubiquitous in our sensorimotor interactions, arising from factors such as sensory and motor noise and ambiguity about the environment. Setting it apart from previous theories, a quintessential property of the Bayesian framework for making inference about the state of world so as to select actions, is the requirement to represent the uncertainty associated with inferences in the form of probability distributions. In the context of sensorimotor control and learning, the Bayesian framework suggests that to respond optimally to environmental stimuli the central nervous system needs to construct estimates of the sensorimotor transformations, in the form of internal models, as well as represent the structure of the uncertainty in the inputs, outputs and in the transformations themselves. Here we review Bayesian inference and learning models that have been successful in demonstrating the sensitivity of the sensorimotor system to different forms of uncertainty as well as recent studies aimed at characterizing the representation of the uncertainty at different computational levels.

Risk-sensitive optimal feedback control accounts for sensorimotor behavior under uncertainty.

Many aspects of human motor behavior can be understood using optimality principles such as optimal feedback control. However, these proposed optimal control models are risk-neutral; that is, they are indifferent to the variability of the movement cost. Here, we propose the use of a risk-sensitive optimal controller that incorporates movement cost variance either as an added cost (risk-averse controller) or as an added value (risk-seeking controller) to model human motor behavior in the face of uncertainty. We use a sensorimotor task to test the hypothesis that subjects are risk-sensitive. Subjects controlled a virtual ball undergoing Brownian motion towards a target. Subjects were required to minimize an explicit cost, in points, that was a combination of the final positional error of the ball and the integrated control cost. By testing subjects on different levels of Brownian motion noise and relative weighting of the position and control cost, we could distinguish between risk-sensitive and risk-neutral control. We show that subjects change their movement strategy pessimistically in the face of increased uncertainty in accord with the predictions of a risk-averse optimal controller. Our results suggest that risk-sensitivity is a fundamental attribute that needs to be incorporated into optimal feedback control models.