This approximation is valid if the probability of correct replication per base (denoted by q) is sufficiently large so that d is small.
The performance of this algorithm is compared with the results of a Gaussian approximation-based approach that aims to determine the probability of correct block size estimation theoretically.
However, for the sparse approximation of My to recover the correct support I, we do not only need that the signal is very sparse S≪d but also that damaged dictionary M Φ remains incoherent, which translates to the original atoms having small supremum norm, ∥ϕ∥ ∞ ≪1.
One implication of the MC approximation being correct is that, given an impute { X obs, X ^ mis }, the distribution p (θ | X obs, X ^ mis ) is well-approximated, i.e., the sampling model is correct.
This concludes that retaining higher moment information can improve the accuracy of approximation and estimate correct parameter values.
Approximation is correct if the difference of the distance between automatically designated point is not bigger than 0.2 Muld from the manual one.
The Taylor series linearization approach (48, 49), which derives a linear approximation of variance estimates to develop corrected standard errors and confidence intervals, was implemented to estimate variances.
As a negative control the entire inner/outer cross-validation loop was repeated with 100 permutations of the sample labels, which gave an approximation of the P-value for the correct classification rate.
Given an estimand of interest θ (e.g., a model parameter), multiple imputation (MI) aims at producing a correct Monte Carlo (MC) approximation of p (θ | X obs ) = ∫ p (θ | X obs, X ^ mis ) p (X ^ mis | X obs ) d X ^ mis from m imputes of X, with X ^ mis denoting some imputation of X mis.
However, a full deterministic model of the first expression product (X) is built in order to: (1) check if the approximation is correct, and (2) make a good setup of the parameters in equations.
