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In this work, we consider a Monte Carlo integration technique based on bias magnitude sampling.
For each of the unknown parameters, which represent the binding affinities of the components and the concentration of polymerase, we searched over a prior parameter space spanning five orders of magnitude, sampling on a log scale between −3 and 2. A typical simulation with a parameter set drawn from the full posterior distribution is shown in Fig. 3D.
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The multiple model algorithm is also used to update the prior information for each bias magnitude sample.
SERS studies of the rhodamine 6G deposited on initial and covered MIFs showed that after the ALD of a 3-nm TiO2 spacer the measured SERS signal dropped about 1.5 orders of magnitude (samples annealed in hydrogen at 150°C, 250°C, and 300°C), as is illustrated in Figure 6.
By increasing the threshold level, the low magnitude samples (including noise and harmonics) are eliminated and high energy samples are used for sampling.
The distance between the point of light entry and exit (optode separation) will determine the magnitude of sampled tissue.
The mHSP72 response occurred to a similar magnitude when sampled at similar time points to those reported in other studies [ 33, 34].
The dense whole-genome predictors act as proxies of pedigree information and can often achieve higher prediction accuracy than the GWAMA-based polygenic score, despite using two orders of magnitude fewer samples (<3000 samples versus >100 000 samples, respectively) and lower coverage of the genome (<268 000 genotyped SNPs versus >2 000 000 SNPs tested for association in GWAMAs, respectively).
In these experiments, SHMC achieves an order magnitude speedup in sampling efficiency for medium sized proteins.
For instance, to achieve the same accuracy of volume estimation in d = 15 dimensions, the combination of MEBS and OEAMC used approximately 2-fold smaller samples than the OEAMC alone (and 17 order of magnitude smaller samples than uniform sampling).
The empirical distribution of the max LOD score under the null is estimated by repeatedly sampling the magnitude of the max LOD score across random permutations of the phenotype data.
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