Sentence examples for using the Laplace approximation from inspiring English sources

The integral can be approximated using the Laplace approximation, see (31– 31).

All analyses were performed in R 2.8.1; all GLMMs were calculated using the Laplace approximation implemented in the lme4 package for R, and use a quasipoisson error structure to account for non-normal errors and overdispersion.

This function performs the fit by using the Laplace approximation, and the correlation structure within the random effects has only an additional constraint: the variance-covariance matrix must be symmetric and positive semidefinite [20].

We fit this model using the Laplace approximation via the glmer function in the lme4 package [Bates et al., 2012] in R [R Development Core Team, 2010].

Model fit is evaluated using the Laplace approximation to the model evidence for varying values of K (the number of Dirichlet components).

Due to survival being binary data, the binomial distribution was selected with a logit link function, and models were fitted using the Laplace approximation.

We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a single-loop Monte Carlo method that uses the Laplace approximation of the return value of the inner loop.

When N is large enough, Eq. (13) can be obtained by using the Laplace-DeMoivre approximation {P}_{mathrm{Fa}}=Qleft(frac{T-N{p}_{fi}}{sqrt{N{p}_{fi}left 1-{p}_{fi}left 1-{pight) (14).

PROC GLIMMIX DATA = SG_DSR METHOD = LAPLACE;/*Specifies using the Laplace method of approximating the log likelihood*/.

For this purpose, this article presents a new approximation for solving the fractional differential equations using the Laplace transform method.

Using the Laplace transform we get (2.15).