Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can yield significant insights into the dynamical organization of the system being investigated. Since experimental measurements are inevitably contaminated by noise, it is thus important to understand the effects of such noise on Granger causality estimation. The first goal of this paper is to provide an analytical and numerical analysis of this problem. Specifically, we show that, due to noise contamination, (1) spurious causality between two measured variables can arise and (2) true causality can be suppressed. The second goal of the paper is to provide a denoising strategy to mitigate this problem. Specifically, we propose a denoising algorithm based on the combined use of the Kalman filter theory and the Expectation-Maximization (EM) algorithm. Numerical examples are used to demonstrate the effectiveness of the denoising approach.

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.

Most of the signals recorded in experiments are inevitably contaminated by measurement noise. Hence, it is important to understand the effect of such noise on estimating causal relations between such signals. A primary tool for estimating causality is Granger causality. Granger causality can be computed by modeling the signal using a bivariate autoregressive (AR) process. In this paper, we greatly extend the previous analysis of the effect of noise by considering a bivariate AR process of general order p. From this analysis, we analytically obtain the dependence of Granger causality on various noise-dependent system parameters. In particular, we show that measurement noise can lead to spurious Granger causality and can suppress true Granger causality. These results are verified numerically. Finally, we show how true causality can be recovered numerically using the Kalman expectation maximization algorithm.

We compare two popular methods for estimating the power spectrum from short data windows, namely the adaptive multivariate autoregressive (AMVAR) method and the multitaper method. By analyzing a simulated signal (embedded in a background Ornstein-Uhlenbeck noise process) we demonstrate that the AMVAR method performs better at detecting short bursts of oscillations compared to the multitaper method. However, both methods are immune to jitter in the temporal location of the signal. We also show that coherence can still be detected in noisy bivariate time series data by the AMVAR method even if the individual power spectra fail to show any peaks. Finally, using data from two monkeys performing a visuomotor pattern discrimination task, we demonstrate that the AMVAR method is better able to determine the termination of the beta oscillations when compared to the multitaper method.

Background and Objective: In numerous occasions the recorded Neural signals are often contaminated by Noise from various intrinsic and extrinsic sources of the system. The noisy data can often give deceptive results when statistical analysis is performed on them. Hence, denoising the contaminated signal by filtering or otherwise is very important to get meaningful results. Several denoising techniques such as Kalman Filtering in conjunction with Expectation-Maximization (KEM algorithm), Levinson-Wiggins-Robinson (LWR) algorithm among others were developed in the recent past. This gave rise to a need for making “a comparative study on the performance of various noise removal methods” to assess their effectiveness.