Sentence examples for expectation approximation from inspiring English sources

begin{aligned} {tilde{J}}(x_t) = underset{u in U_t(x_t)}{min } left{ g(x_t, u) + {{tilde{V}}_t}(x_t^{u}) right} end{aligned} (5 where (x_t^{u}) is the post decision state at time t (i.e. the state after applying controls u but before applying the stochastic variations (w_t) [48]); ({{tilde{V}}_t}(cdot )) is the expectation approximation.

We evaluated the precision and the accuracy of parameter estimates obtained on 500 replication of this trial using the stochastic approximation expectation-approximation algorithm which appropriately handles BLD data.

Data of each simulated trial were analyzed using MONOLIX version 4.2 (http://www.lixoft.eu/monolix/product-monolix-overview/) [ 21], a software devoted to maximum likelihood estimation of parameters in NLMEM using an extension of the stochastic approximation expectation-approximation (SAEM) algorithm [ 22, 23].

Plan et al. investigated parametric approaches for maximum likelihood estimation: first-order conditional estimation in NONMEM and R, LAPLACE in NONMEM and SAS, adaptive Gaussian quadrature in SAS, and stochastic approximation expectation maximization in NONMEM and MONOLIX (both stochastic approximation expectation maximization approaches with default and modified settings).

Data sets were analyzed with NONMEM 7.2 using first-order conditional estimation with interaction and stochastic approximation expectation maximization algorithms.

The biological model parameters were estimated using stochastic approximation expectation maximization followed by importance sampling as implemented in NONMEM 7.3.0 (ICON Development Solutions).

The stochastic approximation expectation maximization method with importance sampling as implemented in NONMEM was used to obtain the estimates of standard errors for the biological models in our analysis, because of numerical difficulties with the first-order conditional estimation method.

24 Estimations were made by maximizing the likelihood of the data, using the stochastic approximation expectation maximization algorithm followed by importance sampling to obtain the objective function value for hypothesis testing.

Estimations were made by maximising the likelihood of the data, using the Stochastic Approximation Expectation Maximization algorithm followed by an important sampling to obtain the objective function value for hypothesis testing by the likelihood ratio test (Beal et al, 2009).

Parameters (Hb0, PLT0, koutPLT, koutHb, IC50Peg-IFN, IC50RBV) were estimated using longitudinal data analyzed by nonlinear mixed-effect models with the Stochastic Approximation Expectation Minimization (SAEM) algorithm in MONOLIX v. 4.2 (http://www.lixoft.eu), assuming exponential random effects models and additive error models.

The performance of stochastic approximation expectation maximization method was sensitive to the initial conditions as reported by Plan et al., 22 and only when we set initial values as the true values, could we get good convergence rates (>99%) for the TQT study design.