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Existing methods for parameter estimation typically make assumptions regarding the form of the Likelihood, and will often ignore any uncertainty around estimated values.
In addition, this study's predecessors focused on implications of national policies limiting carbon emissions, while we do not make assumptions regarding future carbon policy initiatives.
Factorial analyses were performed with a permutation version of ANOVA, which does not make assumptions regarding the distribution of observed data, using the lmPerm R package (https://cran.r-project.org/web/packages/lmPerm/vignettes/lmPerm.pdf).org/web/packages/lmPerm/vignettes/lmPerm.pdf
The acceleration parameter q z) and the expansion rate H z) or dimensionless expansion rate E z) can be determined directly from the data without having to make assumptions regarding the nature or evolution of the "dark energy".
However, this does not suffice to define the process (p^{g} x,mathcal {C})) and thus in the next result we will make assumptions regarding the BSDE (64).
If the uniqueness of the resultant piezomagnetic field is still assured without the need to make assumptions regarding the directions of initial magnetization, the efficiency of studies on the piezomagnetic field would be enhanced.
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One main advantage of using this method relative to others is that results can be obtained without making assumptions regarding the architecture of the ANN model used.
The street sweeper resources (make/model and quantity available) in Auckland were not available for this study, so we made assumptions regarding volume capacities of sweeper trucks, the number of sweeper trucks, and speed of street sweeping (Table 4).
The study design does not allow for making assumptions regarding causality.
Making assumptions regarding the distribution of exposure over time at risk and time not at risk is difficult.
Each of these approaches makes assumptions regarding the missing data that cannot be verified from the observed data.
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