Hierarchical Bayesian Modeling of the Relationship between Task Related Hemodynamic Responses and Neuronal Excitability: a Simultaneous fNIRS/TMS Study

Background: Investigating the relationship between task-related cortical hemodynamic activity and brain excitability is challenging because it requires simultaneous measurement of brain hemodynamic activity while applying non-invasive brain stimulation. There is also considerable inter-/intra-subject variability which both brain excitability and task-related hemodynamic responses are associated with. Here we proposed hierarchical Bayesian modeling to taking into account variability in the data at the individual and group levels, aiming to provide accurate and reliable statistical inferences on this research question. Methods: We performed a study on 16 healthy subjects with simultaneous Paired Associative Stimulation (Inhibitory PAS10, Excitatory PAS25, Sham) and functional Near-Infrared Spectroscopy (fNIRS) targeting the primary motor cortex (M1). PAS was applied to modulate the cortical function and induce plasticity. Before and after each intervention cortical excitability was measured by motor evoked potentials (MEPs), and the motor task-related hemodynamic response was measured using fNIRS. We constructed three models to encode 1) PAS effects on the M1 excitability; 2) PAS effects on the whole-time course of fNIRS hemodynamic responses to finger tapping tasks, and 3) the correlation between PAS effects on M1 excitability and PAS effects on task-related hemodynamic responses. Results: Significant increase of the cortical excitability was found after PAS25, whereas a small reduction of the cortical excitability was shown after PAS10 and no changes after sham. We found PAS effects on finger tapping evoked HbO/HbR within M1, around the peak of the hemodynamic time courses. Both HbO and HbR absolute amplitudes increased after PAS25 and decreased after PAS10. Cortical excitability changes and task-related HbO/HbR changes showed a high probability of being positively correlated, 0.77 and 0.79, respectively. The corresponding Pearson correlations were 0.58 (p<.0001, HbO with MEP) and 0.56 (p<.001, HbR with MEP), respectively. Conclusion: Benefiting from this original Bayesian data analysis, our results showed that PAS modulates task-related cortical hemodynamic responses in addition to M1 excitability. The fact that PAS effects on hemodynamic response were exhibited mainly around the peak of the hemodynamic time course may indicate that the intervention only increases metabolic demanding rather than modulating hemodynamic response function per se. Moreover, the positive correlation between PAS modulations of excitability and hemodynamic brings insights to understand the fundamental properties of cortical function and cortical excitability.

Hierarchical Bayesian Modeling and Randomized Response Method for Inferring the Sensitive-Nature Proportion

In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of the SNP is obtained via using a hierarchical Bayesian modeling procedure. Moreover, a hybrid algorithm using Gibbs sampling in Metropolis–Hastings algorithms is used to obtain the Bayes estimator of the SNP. The highest posterior density interval of the SNP is obtained based on the empirical distribution of Markov chains. We use the term 3RR-HB to denote the proposed method here. Monte Carlo simulations show that the quality of 3RR-HB procedure is good and that it can improve the drawback of the maximum likelihood estimation method. The proposed 3RR-HB procedure is simple for use. An example regarding the homosexual proportion of college freshmen is used for illustration.

Comparing measures of sensitivity for vigilance tasks: Bayesian-estimated and log-linear corrected measures outperform A!

Signal detection analyses often attribute the vigilance decrement to a combination of bias shifts and sensitivity losses. In many vigilance experiments, however, false alarm rates are at or near zero, complicating the analysis of sensitivity. Here, we report Monte Carlo simulations comparing three measures of sensitivity that can be calculated even with extreme hit and false alarm rates: A’, an estimate of the area under the curve that is commonly but mistakenly described as nonparametric; Az calculated using the log-linear correction, a statistic that adjusts individual observers’ data to protect against low false alarm rates; and, 4z estimated using a Bayesian hierarchical procedure, a measure that protects against extreme false alarm rates by sharing information between observers. Results confirm that bias shifts produce spurious changes in A’, and demonstrate that, 4z estimated with either a log-linear correction or through hierarchical Bayesian modeling is more robust against low false alarm rates.