Not exact matches
For the LTQ - Orbitrap Velos
data, the
distribution of mass deviation (from the theoretical masses) was first determined as having a standard deviation (σ) of 2.05 part per million (ppm), and a mass
error of smaller than 3σ was used in combination with Xcorr and ΔCn to determine the filtering criteria that resulted in < 1 % false positive peptide identifications.
Tim Beatty, Random sampling
errors are actually fairly well understood, even for «
distribution - free» cases, and if you have enough
data, this isn't really a problem.
The ``... uneven spatial
distribution, many missing
data points, and a large number of non-climatic biases varying in time and space» all contribute inaccuracies to to the global temperature record — as do
errors in orbital decay corrections, limb - corrections, diurnal corrections, and hot - target corrections, all of which rely on measurements (+ - inherent
errors), in the satellite temperature records.
When theoretical
distributions are not available for this purpose, Monte Carlo experiments with randomly - created
data containing no climatic information have been used to generate approximations of the true threshold values (Fritts, 1976; cf. MM05a; Huybers, 2005; Ammann and Wahl, in review — note that the latter two references correct
errors in implementation and results in MM05a)(A&W, p. 45)
The PDF has been computed in the same way (apart from the reciprocal relationship) as the climate sensitivity PDF in Figure 2 in the original paper, using the same
data and
error distribution assumptions but with a larger number of random samples to improve accuracy.
The whole point of the discussion was your claim that statistics can improve the precision of the
data without having a clue of whether the
errors are normally distributed or of some known
distribution.
The Forster / Gregory 06 results were obtained and presented in a form that accurately reflected the characteristics of the
data, with
error bands and details of
error distribution assumptions, so permitting a valid PDF for S to be computed, and compared with the IPCC's version.
The problems with ECS
distributions most often involve use of inappropriate prior
distributions, so that the ECS
distribution obtained does not properly reflect the
error distributions of the underlying
data.
The difference between iid and LTP, for example, is confined to the covariance matrices of the corresponding
error distribution (the covariance matrix corresponding to iid
data is simply an identify matrix multiplied by a scalar variance; for LTP, the off - diagonal elements are non-zero and non-vanishing).
I know how tempting it is to assert (or rather, hope) that an average might cancel some of the
errors made by each of the three methods, but as long as they share
data they are in no sense independent, as long as the are based on differing methodology the are in no sense identically distributed, and there is no theorem or sound argument I can imagine that
errors in methodology are unbiased, zero sum white noise drawn from some trendless
distribution.
This has nothing to do with autocorrelation in
data,
error distributions, or lucia's use of Cochrane - Orcutt.
The answer is, man - made global warming supporters simply wave their hands in the air, assume Gaussian or near - Gaussian
distribution of
errors from a multitiude of very complex, biased sources, declare they cancel out, and that aggregation and division allow them to generate a result with 0.00 accuracy even though the input
data can not be measured to that degree of accuracy.
That's just one example of how you get non-Gaussian
error distribution in the
data.
The law of large numbers requires
data sources to be free of bias, and the
errors to be Gaussian in
distribution.
If you have a solid understanding of the
distribution of the
errors and you have enough
data points, it's actually pretty straightforward.
All of statistics are based on mathematics derived from assumptions about probability
distributions, and how
data and
errors in measured
data might follow them.
If you know the standard -
errors of the various
data - point (i.e. global mean temperature) estimates, we can check if it's statistically significant via a difference in means test, while accounting for correlation in estimator
distributions (it should be, unless NASA can't measure at all, which I sincerely doubt).
[26][27][29][30] They give
distribution - free expressions for direct and indirect effects and demonstrate that, despite the arbitrary nature of the
error distributions and the functions f, g, and h, mediated effects can nevertheless be estimated from
data using regression.