Analogs for derivatives are defined, differential equations are replaced by difference equations, an analog in terms of finite differences is derived of the Taylor series and most of classical physics can be imitated.
No longer-term revisions are assumed to be required, because the SPG stimulation system does not have a battery that needs to be replaced, a difference to other stimulation technologies such as spinal cord stimulation (SCS) and occipital nerve stimulation (ONS).
Hence, for Bayesian approach, penalized splines are introduced by replacing the difference penalties with their stochastic analogues.
In the Bayesian approach, penalized splines are introduced by replacing the difference penalties with their stochastic analogues, i.e., first or second order random walk priors for the regression coefficients.
However, the information on the directionality would be missed if difference were replaced by absolute difference.
To determine why SUMO is not capable of functionally replacing SLD2, differences between the two were sought.
Eq. (3) can then be rewritten as: <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0005372.e028.PNG" class= inline-graphic"/> It is convenient to take the continuous limit, replacing finite differences by derivative, and sums by integrals.
For difference-in-difference estimates, Y1i is replaced by the difference between earnings following participation and earnings prior to program participation, and Y ¯ 0 j i is replaced by the average difference for the matched comparison cases over the same period.
In field applications, it is difficult to measure the injection pressure difference, so the wellhead pressure is often used to replace the injection pressure difference to determine the injectivity index.
In the next section, our variant of this experiment is described, in which the difference between sleep and wake is replaced by the difference between virtual training and no virtual training.
