Denoising neural data with state-space smoothing: Method and application

Neural data are inevitably contaminated by noise. When such noisy data are subjected to statistical analysis, misleading conclusions can be reached. Here we attempt to address this problem by applying a state-space smoothing method, based on the combined use of the Kalman filter theory and the Expectation–Maximization algorithm, to denoise two datasets of local field potentials recorded from monkeys performing a visuomotor task. For the first dataset, it was found that the analysis of the high gamma band (60–90 Hz) neural activity in the prefrontal cortex is highly susceptible to the effect of noise, and denoising leads to markedly improved results that were physiologically interpretable. For the second dataset, Granger causality between primary motor and primary somatosensory cortices was not consistent across two monkeys and the effect of noise was suspected. After denoising, the discrepancy between the two subjects was significantly reduced.

Continuously equivalent networks in state space

Schoeffler has derived continuously equivalent networks in the nodal-admittance domain. The letter derives a corresponding result in state space that combines the usefulness of Schoeffler's result and the power of the state-variable approach.

Zero-sum risk-sensitive stochastic games on a countable state space

Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron-Frobenius eigenvalue of the associated controlled nonlinear kernels. (C) 2013 Elsevier B.V. All rights reserved.

Bayesian parameter identification in dynamic state space models using modified measurement equations

When Markov chain Monte Carlo (MCMC) samplers are used in problems of system parameter identification, one would face computational difficulties in dealing with large amount of measurement data and (or) low levels of measurement noise. Such exigencies are likely to occur in problems of parameter identification in dynamical systems when amount of vibratory measurement data and number of parameters to be identified could be large. In such cases, the posterior probability density function of the system parameters tends to have regions of narrow supports and a finite length MCMC chain is unlikely to cover pertinent regions. The present study proposes strategies based on modification of measurement equations and subsequent corrections, to alleviate this difficulty. This involves artificial enhancement of measurement noise, assimilation of transformed packets of measurements, and a global iteration strategy to improve the choice of prior models. Illustrative examples cover laboratory studies on a time variant dynamical system and a bending-torsion coupled, geometrically non-linear building frame under earthquake support motions. (C) 2015 Elsevier Ltd. All rights reserved.

Risk-Sensitive Ergodic Control of Continuous Time Markov Processes With Denumerable State Space

In this article, we study risk-sensitive control problem with controlled continuous time Markov chain state dynamics. Using multiplicative dynamic programming principle along with the atomic structure of the state dynamics, we prove the existence and a characterization of optimal risk-sensitive control under geometric ergodicity of the state dynamics along with a smallness condition on the running cost.

Sequential Monte Carlo computation of the score and observed information matrix in state-space models with application to parameter estimation

Sequential Monte Carlo (SMC) methods are popular computational tools for Bayesian inference in non-linear non-Gaussian state-space models. For this class of models, we propose SMC algorithms to compute the score vector and observed information matrix recursively in time. We propose two different SMC implementations, one with computational complexity $\mathcal{O}(N)$ and the other with complexity $\mathcal{O}(N^{2})$ where $N$ is the number of importance sampling draws. Although cheaper, the performance of the $\mathcal{O}(N)$ method degrades quickly in time as it inherently relies on the SMC approximation of a sequence of probability distributions whose dimension is increasing linearly with time. In particular, even under strong \textit{mixing} assumptions, the variance of the estimates computed with the $\mathcal{O}(N)$ method increases at least quadratically in time. The $\mathcal{O}(N^{2})$ is a non-standard SMC implementation that does not suffer from this rapid degrade. We then show how both methods can be used to perform batch and recursive parameter estimation.