Finally, we calculated the Wilmott's index of agreement (d): d = 1 - frac{{mathop sum nolimits_{i = 1}^{n} (X_{i} - Y_{i} )^{2} }}{{(|X_{i} - underline{X} | + |Y_{i} - underline{X} |)^{2} }}Xwhere Xi was the biomass estimate for state i estimated from FIA plot data and Yi was the same estimated from the maps [29].
In all cases, when drift parameter μ was included the MCMC chain mixed well and arrived at the same estimated posterior distribution from different starting points.
For example, two of the sites (Wolfville, NS and McCarthy, AK) had the same estimated bedrock age (300 my) but significantly different mean 87Sr/86SrF ratios (1-tailed t-test; t5 = −3.82, P = 0.006).
A brass-trimmed table made with a type of walnut, top, has an estimated auction price of $27,000 to $36,500; a cabinet, above, made with the walnut, painted wood, steel and brass, comes with wall paneling and the same estimate.
The same is true for all normal derivatives of (u_1), and the same estimates hold as in the case of positive (s>0) (cf. [8] and [12]).
Despite the minor change in InChIKey layout upon transition from InChI Software v. 1.02-beta to v. 1.03 and further, this level remained the same and the same estimate was quoted with each new release [3]: "Note that due to the very essence of hash functions, collisions (the same InChIKey for different InChIs/structures) are unavoidable in very large collections.
Indeed, let (T inmathcal{T}_{h}) be a mesh element, then by the multiplicative trace inequality [12], Theorem 1.6.6, (lVert mathbf {A} rVert_{L^{2}(partial T ^{3}} < C_{mathrm{tr}} lVert mathbf {A} rVert_{L^{2}(T)^{3}}^{1/2} lVert mathbf {A} rVert_{H^{1}(T)^{3}}^{1/2}), and the same estimate holds for (nablatimes mathbf {A}).
Upon review, it was surprising that the point estimates in Model A, ignoring stratification and clustering, were invariant of ICC, and that the same estimates were returned by four patient-level models for each simulation.
A sensitivity analysis was used to test the reliability of the results, and it reported that the results remained unchanged and had the same estimates after deleting any one of the included studies.
It is perhaps even more remarkable and carried the same estimate.
We repeated the experiments above for the D > P model with n = 10000 and q = 0.0125 and for the D=P model using k max = 22 for this algorithm, and obtained the same estimates of m G,0.99reported above.
