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These approaches are very fast, work well in the near-field, and give some of the most accurate head pose estimates in practice.
We note that while finding a model that can describe the time series well is of value, good explanatory power does not necessarily imply that the model can be used to make estimates in practice.
Although we find that high-resolution geophysical data are useful for obtaining these estimates, in practice, geophysical profiles often sample only a small portion of the aquifer under investigation, and thus, the estimates obtained from geophysical data may not be sufficient to completely describe the hydraulic properties of the aquifer volume.
Lastly, with much of the attention on species-tree analyses focused on the discord among loci arising from the coalescent, this work also highlights a previously overlooked key determinant of species-tree accuracy for recent divergences – the level of genetic variation at a locus, which has important implications for improving species-tree estimates in practice.
We describe in the appendix two approaches for rescaling estimates in practice to allow direct comparisons between NLMMs and SEMs or to compute mediated effects via NLMMs only.
While (A1) essentially follows from the triangle inequality and appropriate inverse estimates in practice, the reduction (A2) builds on the observation that the element sizes of the sons of a refined element uniformly decreases.
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In addition, the proposed method does not rely on computing vanishing points, which is difficult to estimate in practice.
Thus, even very irregular variations of the Hölder regularity of the GMBM may be detected and estimated in practice.
The beam broadening of the Doppler peaks is proportional to the background wind speed, estimated in practice after a time averaging over ~30 min.
However, it is also well known that empirical MFDs are not easy to estimate in practice due to difficulties in obtaining the requisite data needed to construct them.
All these functions enjoy some smoothness, but at the very beginning, to use this smoothness we need second-order or third-order derivative information of the problem function that is difficult to estimate in practice.
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