Indeed, setting L to a prescribed upper bound on the model order, one may further regularize the cost in (12) to impose sparse AR coefficient vectors; that is, { a ^ n } n = 0 N = arg min { a n } n = 0 N 1 2 y - Ma 2 2 + λ ∑ n = 1 N a n - a n - 1 2 + γ a 1. (38).
Starting from the model uncertainty of the local sample to sample LTI or LTV models, and using the randomized algorithm, we compute the bound on the model uncertainty of the ILC system representation in the trial domain (lifted ILC).
We employ the explicit time and input dependent bound on the model order reduction error to achieve design conditions for constraint fulfillment, recursive feasibility and asymptotic stability for the closed loop of the model predictive controller when applied to the high-dimensional system.
Below we explore different choices for fMRI priors, evaluating them quantitatively by T-tests of the negative free-energy bound on the model log-evidence, and qualitatively in terms of the optimized hyperparameters, source reconstructions, and source time courses.
Using the free-energy bound on the model evidence, we showed how the SPM{F} from a group of 18 participant's fMRI data in MNI space could improve standard minimum-norm inversions of MEG and EEG data from a different group of 12 participants.
The bias and variance of the estimated model parameters are analysed and a frequency domain bound on the modelling error is estimated.
The maximized F is a lower bound on the log model evidence, namely the probability of the data given the model (Stephan et al. 2009).
We also find the maximum error bound of the approximation in the model space R3; and the bound on the distance, in model space, between the approximations which come from the domain of each surface.
Full models place an upper bound on the complexity and size of the model space and should thus be no more complicated than needed to answer the question of interest, e.g. models with a fourth ATP binding site should not be considered as there is no evidence that such a site exists.
In Section 11 in Supplementary Material, we prove an upper bound on the probability of our model predicting any bias, if the experiment is in fact unbiased, showing that there very little risk in the applying the method to an unbiased data set.
