Although our method relies on assumptions known not to hold exactly, approximate model permits the implementation of a fast and stable algorithm that greatly improves downstream results.
The approach is a computational one in which quantities that are intractable to evaluate exactly are approximated by sample averages from randomized algorithms.
Queries are run exactly and approximated by unspecifying one, two and all node labels and replacing one edge with an approximate path constrained to less than 3 and 7 edges.
The Fisher's exact test has more power than a chi-square test when there are low expected values, because the significance is measured exactly, not approximated (Agresti, 1992).
The method requires the lowest-eigenvalue eigenvector of the Hessian which can be calculated exactly or approximated by a method such as the dimer method, Lagrange multipliers,or the Lanczos method.
Although the distribution used for simulating the QTL effects and that used for analysing the data did not agree exactly, 'BayesB' approximates the prior distribution of the QTL effects better than the regression methods.
What are the arguments for using this model (other than that it seems to work post factum, e.g., reproduce the linear slope, etc).? This model serves as a basis of approximation, so what exactly is being "approximated" in this approach, i.e., what is disregarded and what is kept?
This indicates that ( {widehat{sigma}}_{Ri}^2 ) is not exactly the variance of approximated Gaussian distribution of ( {widehat{boldsymbol{n}}}_{Ri}={sigma}_{Ri}^2+{P}_R{h}_{Ri}^2{beta}^2{sigma}_{tilde{n}}^2 ).
In general, the term ((f,phi_{j})) cannot be computed exactly and is usually approximated by ((I_{N}f,phi_{j})), where (I_{N}) is an interpolation operator upon (P_{N}) relative to the Gauss Lobatto points.
The length of rectangle E seemed to clearly be approximating exactly 0.60000000…, even when estimated to a dozen decimal places.
