English

Abstract

Keywords: Fisher information, Cramer-Rao bound, Fisher metric, movement control, minimum variance model, proportional noise, signal dependent noise. Abstract: Fisher information places a bound on the error (variance) in estimating a parameter. The nervous system, however, often has to estimate the value of a variable on different occasions over a range of parameter values (such as light intensities or motor forces). We explore the optimal way to distribute Fisher information across a range of forces. We consider the simple integral of Fisher information, and the integral of the square root of Fisher information because this functional is independent of re-parameterization of force. We show that the square root functional is optimised by signal-dependent noise in which the standard deviation of force noise is approximately proportional to the mean force up to about 50% maximum force, which is in good agreement with empirical observation. The simple integral does not fit observations. We also note that the usual Cramer-Rao bound is ‘extended’ with signal-dependent noise, but that this may not be exploited by the biological motor system. We conclude that maximising the integral of the square root of Fisher information can capture the signal dependent noise observed in natural point-to-point movements for forces below about 50% of maximum voluntary contraction.