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Section 4 contains recent advances concerning the applicability of the chaos game, one of two main algorithms for drawing an accurate approximation to an attractor of an IFS.
Common software methods in the early 1990s drew a first approximation from a lookup table.
Although condition (2) in Definition 2.2 can be used as the basis of an algorithm to draw arbitrarily accurate approximations to an attractor of an IFS, such a method is inefficient because the number of computations grows exponentially with k.
The paper explores the implications of perfect prediction for MI using monotone or MICE imputation with the "Normal-approximation draw" method, and proposes several solutions.
One way to improve the approximation is to use importance sampling in which several values of θ ∗ are drawn from the Normal approximation, and the values of R are computed and used in choosing one of the θ ∗ values (Rubin, 1987b, 2003).
The single "Fireflies" drew ire for its approximation of the Postal Service (the similarities do feel somewhat egregious), but it's the song's lyrics ("I get a thousand hugs, from 10,000 lightning bugs/As they try to teach me how to dance") that might really make you squirm.
The importance sampler that we consider draws from the Euler approximation of the SDE ([24]).
A static FEM model setting a beams secant elastic modulus (E/3) and semi-rigid internal nodes drew with an adequate approximation the experimental behavior.
Then, N particles are drawn from the Gaussian approximation of prediction: {boldsymbol{X}^{n}_{k} sim mathcal{N}(boldsymbol{x}_{k};~boldsymbol{bar{x}}_{k|k-1},~boldsymbol{P}_{k|k-1})}^{N}_{n=1}.
In fact, β * is drawn from the asymptotic approximation to its posterior distribution, and the imputed values are only approximate draws from the posterior predictive distribution of the missing data.
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