To investigate in more detail the mechanisms underlying these statistical results, we performed simulations in which a single realization is followed along the time, without any averaging.
To give some intuition on the operation and performance of the PF method in Algorithm 1, we show the results for a single realization in Fig. 2.
It is shown how the average over the ensemble of realizations of the surface profile function used in the design of these surfaces can be replaced in the theory and in experiment by the illumination of a single realization of the random surface by a broadband source.
In this context, D AI and D IA are averages of log-likelihood ratios, as opposed to an evaluation at a single realization (in ML estimation parameters vary whereas observations are taken as fixed).
The microtubules in the oocyte are highly dynamic and a single realization of the MT cytoskeleton would be unrepresentative of the many alternative MT configurations that oskar mRNA samples during the 6-9 hour period of its localization.
Another essential difference is that for many environmental flows it is essential to make forecasts-detailed predictions of the actual state (i.e., a single realization) for some time in the future.
Syeed and Jones (26) also demonstrated that the formulation presented in equation 5 might also be utilized when a single realization of the analyzed stochastic process is available, as is the case when processing surface myoelectric signals recorded dynamic contractions.
As shown in Additional file 3: Figure S3, MIRI values for a single realization of the parameters L H S sampling (Additional file 3: Figure S3A) and MIRI box plot for 100 realization (Additional file 3: Figure S3B) suggested that two parameters are relevant for this evaluation function: k12 and λ.
