For simple models, an analytical formula for the likelihood function can typically be derived.

However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate.

Various empirical and analytical formulae have also been derived from measurements that are useful approximations.

This is consistent with the analytical formulas for R-tree performance.

No simple analytical formula for general eigenvectors is known.

Comparison between simulation results and analytical formulation-For example, assessing the value of the radar cross section of a plate with the analytical formula:

However, analytical formulae have been worked out for the hydrogen molecular ion (see references herein).

As with many wavelets there is no nice analytical formula for describing these harmonic spherical wavelets.

An analytical formula of the gradient of potential energy is preferentially required by the gradient methods.

The transition wavenumbers cannot be expressed in terms of an analytical formula but can be calculated using numerical methods.