While facilitating an efficient and scalable parameter estimation, a model decomposition involving the linear approximation of the time integral of each rate equation may not result in a high-quality estimate, especially when the model of interest is highly nonlinear or the given time series data are sparse.
Reminding that L is a sum of N independent random variables, asymptotic analysis in probability theory (when N is large enough) shows that bounds similar to (24) and (25) are much more appropriate for estimating α and β than the Gaussian approximation especially when λ is far from E[L], namely when bounding the tails of a distribution [16, 17].
The discrepancy between these estimate arises from two factors: (1) the tomography gives the hmF2 with a resolution of 25 km, whereas the ionosonde estimates are 'point measurements'; (2) the estimate of hmF2 using Eq. (4) is only an approximation to the actual hmF2, especially when the values of ƒ o E are not reliable.
However, when a bifurcation does exist in the mass action kinetics approximation, the question remains open, especially when the parameters are very close to the bifurcation of the mass action kinetics system.
In addition, these exact algorithms allow us to avoid the edge effect observed under the single sequence approximation, which leads to erroneous results, especially when the marginal distribution of the model displays a slow convergence toward the stationary distribution.
Model form uncertainty, inherently existing in selecting the best approximation from a model set cannot be ignored, especially when the predictions by competing models show significant differences.
Despite these factors, it will be shown in Section 6 that the approximation yields relatively close results to the simulation results, especially when the block size is estimated over large number of symbols.
We believe that octyl-2-cyanoacrylate can be used to repair any perineal tear, as long as the tension on the glue is not excessive, especially when the edges do not require approximation.
Odds and risk ratios were combined as indicators of RR, based on the assumption that the odds ratio is an approximation of the risk ratio; this assumption has some limitations, however, especially when the outcome of interest is common (5).
Given the inherent limitations of the Weitzman procedure, especially when the number of breeds is large, the alternative approximation algorithm of Garcia et al. [ 22] was also tested with the 13 geographical breed groups [see Additional file 4: Figure S3] to investigate the partial contributions of each breed to genetic diversity.
