Robust inference and modelling for the single ion channel

Abstract

Statistical modelling and inference for a single-ion channel have principally been carried out using finite-state space continuous-time Markov chains. Statistical inferences for the closed and open dwell times and the kinetic rate constants between states have then been arrived at via maximum likelihood methods, including the use of the EM algorithm. The fundamental assumption behind this theory is that one has the correct number of closed and open states, something which may not be easily determined by the use of current methods for modelling, say, the number of components in a mixture of exponential distributions used to fit, say, the ‘closed’ dwell times. Here, we show that the use of a robust L 2 estimator can outperform the EM algorithm both when the correct number of states is apparent and also when there are small deviations from the supposed models. After describing the statistical models used to demonstrate these results and how they lead to particular mixtures of exponential distributions the comparison is then made between the performances of the estimators (robust L 2 and maximum likelihood (via the EM algorithm)). The resulting performances in terms of means and standard errors of the estimated kinetic rate constants are then assessed. The estimating equations derived from minimizing the L 2 distance are given explicitly in the appendices.