As already mentioned, likelihood scores may be slightly different if model parameters are optimized using the standard approach because of numerical deviations.
One should keep in mind that, numerical deviations in likelihood scores will increase as more computations are omitted by our approach because rounding error propagation will become more prevalent.
E. g. in the simplest case of just 2 copies and 2 haplotypes in an MSV spanning region, relatively small numerical deviations from the theoretical ratio of 1.0 (1:1) may result in quite different minimal CN estimations, as 1.2 (6:5) indicates 11 copies, 1.25 (5:4) indicates 9 and 1.33 (4:3) indicates 7.
Disregarding slight numerical deviations because of round-off errors and a distinct ordering of floating point operations (floating point arithmetics are not associative), the above procedure to compute the likelihood on gene-induced subtrees theoretically yields exactly the same likelihood score as the standard method.
The corresponding post hoc sensitivity analysis restricted to the 178 subjects who completed all treatments and had valid data for all three treatments showed only minor numerical deviations in estimates and did not change the statistical hypothesis evaluations (data not shown).
Due to the construction of municipal engineering in the south of excavation was not considered in numerical simulation, deviation of monitored and simulated settlement of monitoring point DB03 1 is greater than others.
In mathematical terms, we allow for the probability that a food source is in the nearby area to deviate from 1. Initially, this probability was set to be very close to one (within numerical accuracy, deviation from 1 was ∼10−100).
The histology in case 1 revealed a dense population of cortical neurons without substantial numerical and structural deviation from age-matched controls.
A comparison of the results with those obtained from numerical methods shows deviations in the numerical results at high Pe numbers.
The numerical values, standard deviations and t-test values of the wings discussed in this and the previous section are presented in Table S1.
