In the meshfree method, it is important to note that the accuracy and stability of the method is conditional upon the correlation parameter ω, the nodal spacing h (h is the average nodal distance between any two points), and also the Reynolds number Re.
In the E-step the unobserved indicator variables z i j are replaced by their expected values conditional upon the current parameter estimates and the data Y i t e ij = E (Z ij | α j, p j, β, σ 2 ).
This structure facilitates efficient posterior computation, since the full conditional distributions of the parameters have simple conjugate forms.
The first stage obtains the conditional distribution of the nuisance parameter conditional on the parameter of interest.
Both random effects and response values were simulated conditional on the parameter estimates, using 1000 samples.
It is important to note that the posterior distributions listed in Table 2 are conditional upon fixed model parameters (Table 1), prior distributions of calibrated parameters (Table 2), and the data sets used in calibration.
We cast the problem in a probabilistic framework known as modeling field theory (MFT), in which the pdf of the data is composed of a mixture of components, each conditional upon parameters including target positions as well as sensor kinematics.
A value of α near one indicates that the influence of that particular reaction mechanism on AP-1 is not significantly conditional upon other parameter values.
Variance parameters (sigma^{2}_{u}) and (sigma^{2}_{delta }) control the variability of the random effects (U_{i}) and (delta_{i}) conditional upon the random effects in the neighboring municipalities, respectively.
Individual donors were used up to five times, conditional upon the health of an individual animal.
Citizenship, in modern British rhetoric, is conditional upon the money you bring in.
