Monitoring dynamical processes requires the estimation of the entire state, which is only partly accessible by measurements. Most quantities must be determined via model based state estimation, which in general is an ill-posed inverse problem. Regularization techniques have to be applied. In most of the literature the initial data are also regularized. However, the initial data are typically un...

Model-based analyses have become an integral part of modern metabolic engineering and systems biology in order to gain knowledge about complex and not directly observable cellular processes. For quantitative analyses, not only experimental data, but also measurement errors, play a crucial role. The total measurement error of any analytical protocol is the result of an accumulation of single err...

Peter Dayan Brain and Cognitive Sciences E25-210, MIT Cambridge, MA 02139 [email protected] We have calculated analytical expressions for how the bias and variance of the estimators provided by various temporal difference value estimation algorithms change with offline updates over trials in absorbing Markov chains using lookup table representations. We illustrate classes of learning curve...

Bayesian filtering of stochastic stimuli has received a great deal of attention recently. It has been applied to describe the way in which biological systems dynamically represent and make decisions about the environment. There have been no exact results for the error in the biologically plausible setting of inference on point process, however. We present an exact analysis of the evolution of t...

The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the closed-form solutions of conditional entropy without involving any approximation. Two basic types of classification errors are investigated in the context of bin...

In this article, we propose and test a new model for measurement error in analytical chemistry. Often, the standard deviation of analytical errors is assumed to increase proportionally to the concentration of the analyte, a model that cannot be used for very low concentrations. For near-zero amounts, the standard deviation is often assumed constant, which does not apply to larger quantities. Ne...