To my mind this could be a starting point for
a calibration curve for mechanical stress?
Additional file 1: DLS results / TEM histogram /
Calibration curve for sugar quantification / ICP - MS conditions / Carbonyl formation at different concentrations / Extracellular quantification of silver ions.
Not exact matches
I had a Savina placenta sample which of course was miles out of the standard solutions
calibration curve range, and using the equation
for the line got a result.
Rear - wheel steering remains
for the vastly improved agility that it brings, but with a completely different
calibration of the response
curve.
Transmission BorgWarner four - wheel drive Polestar
calibration for more rear torque dynamic distribution Polestar calibrated stability control system 8 - speed Geartronic automatic gearbox with paddle shifters Faster gearshifts
Curve - hold functionality Off - throttle functionality Optimized shift precision
If we do this
for a series of rings through any given chronology, we can then establish a radiocarbon
calibration curve, which allows us to translate any radiocarbon age into a true calendar date.
Moreover, the radiocarbon community has suggested the use of local
calibration curves to better account
for regional MRE offsets in the heterogeneous ocean reservoir, but a reasonable method
for their construction has not yet been proposed.
So in both cases, one can construct a confidence / credible interval
for the carbon - 14 age by well - known methods (that exhibit perfect probability matching), and then simply transform the endpoints of this interval to calendar years using the
calibration curve (which I'll assume is known exactly, since uncertainty in it doesn't seem to really affect the argument).
The flat spot on the
calibration curve represents mean failure time of the widget
for a given activity age of catalyst, invariant until the catalyst starts to fail.
The ground - based Windcube has been deployed
for wind resource assessment, prototype power
curve validation, or site
calibration, whereas the nacelle - mounted Wind Iris has been used
for wind - turbine performance monitoring or prototype and warranty power
curve assessments.
Provided we know the size and shape of the error in that original reading (Normal, log Normal etc) we can generate a spread of random values around our actual reading reflecting what it might be, and then
for each of those read off the age that implies, using a table that randomly selects from the (smeared out)
calibration curve at that value.
An alternative way of seeing that a noninformative prior
for calendar age should be proportional to the derivative of the
calibration curve is as follows.
There is a question, however, of whether the prior should be uninformative or informed, since the uniform prior
for calendar age leads to a prior
for C14 age that is informed by the
calibration curve.
Nor is it whether the prior should be subjective or objective, since
for this purpose the
calibration curve is objective information.
As can be seen, it is very different from the uniform - calendar - year - prior based posterior that would be produced by the OxCal or Calib programs
for this 14C determination (if they used this
calibration curve).
That's the case in Fig. 1, as the most essential requirement
for getting a reasonable confidence interval is to include the whole flat part of the
calibration curve or none of that part.
One can think of there being a nonlinear but exact functional
calibration curve relationship s14C = c (ti) between calendar year ti and a «standard» 14C age s14C, but with —
for each calendar year — the actual (true, not measured) 14C age t14C having a slightly indeterminate relationship with ti.
If the measurement
for carbon - 14 age has Gaussian error with standard deviation 100 (as seems about right
for Nic's Fig. 2), and the measurement is rounded to one decimal place, and the
calibration curve maps calendar age 750 to carbon - 14 age 1000, then the probability of the observation being 1000.0 given that the calendar age is 750 is 0.1 (
for one decimal place) times the probability density at 1000 of a Gaussian distribution with mean 1000 and standard deviation 100, which works out to 0.0004.
For this purpose, it would not be necessary to draw true ages from the full prior, but only well on either side of the selected range, in order to accommodate possible observation error and the distortion of the
calibration curve.
The radiocarbon determination will be more than two standard deviations (of the combined radiocarbon and
calibration uncertainty level) below the exact
calibration curve value
for the true calendar date in 2.3 % of samples.
An error - free laboratory measurement of modern fraction does not imply that the problem collapses into a deterministic look - up from the
calibration curve — even if the
curve is monotonic over the relevant calendar interval — because the
curve itself carries uncertainty in the form of the variance related to the conditional probability of RC age
for a given calendar date.
But it also can't provide conclusive evidence
for the calendar year having any other value, unless there's a calendar year
for which the
calibration curve is nearly vertical, covering the entire range of carbon - 14 ages that are plausible given the measurement.
Suppose
for a moment that the hypothetical
calibration curve came from costly and time - consuming destructive testing of a critical aeroplane component.
But one question
for Nic: How far off is the normalized (f (x)-RRB- where f (x) = g (C (x)-RRB- where C is the
calibration curve, g (y) is the pdf
for the Radio Determined Age and then the normalized (f) is the pdf
for the calendar age, as compared to the Bayesian Posterior using Uniform Prior?
He lays out a proper discretized sample space
for the
calibration curve which allows him to use Bayes formula, there.
the point on the
calibration curve is say, C14age = 2550, CalYear = 800 Now look at the probability measure we have
for the C14age interval = 2550 - 3000 that's at least 40 % of the pink paint and the amount of measure we have
for the corresponding CalYear interval = 800-3000 That's barely 10 % of the grey paint.
The mish mash being discussed here
for the «other techniques» ALSO uses the «uniformly» provided
calibration curve.
For both variants of the uniform prior subjective Bayesian method, probability matching is nothing like exact except in the unrealistic case where the sample is drawn equally from the entire
calibration range — in which case over-coverage errors in some regions on average cancel out with under - coverage errors in other regions, probably reflecting the near symmetrical form of the stylised overall
calibration curve.
Now we find potential SST data that while it may not necessarily change some of the total delta C, it could change the shape of the
curves that are used
for the
calibration period.
The reason
for the form here of Jeffreys» prior is fairly clear — where the
calibration curve is steep and hence its derivative with respect to calendar age is large, the error probability (red shaded area) between two nearby values of t14C corresponds to a much smaller ti range than when the derivative is small.
Professor Bronk Ramsey considers that knowledge of the radiocarbon
calibration curve does give us quantitative information on the prior
for 14C «age».
The latter is a value assumed by the laboratory and then accounted
for in the
calibration curve.
Suppose the transformation from calendar date to 14C age using the
calibration curve is effected before the application of Bayes» theorem to the notional observation
for a uniform prior.
Not only is the frequentist estimation as good, it is the best and an unbiased estimate.It can even experimentally be proved that it is the best.Same
for the
calibration curve pdf.
Note that
for this computation it is not necessary to know the slope of the
calibration curve at calendar age 1000.
The reason given in Briffa 2001
for their selection of a certain reconstruction is discussed: >> > The selection of a single reconstruction of the ALL temperature series is clearly somewhat arbitrary... The method that produces the best fit in the
calibration period is principal component regression... << >> ``... we note that the 1450s were much cooler in all of the other (i.e., not PCA regression) methods of producing this
curve...» << <
I think that a helpful first step would
for the experts to provide a «
calibration curve»
for the Earth's thermostat.
Then, there's the additional problem with the
calibration curve (s)
for each instrument and each frequency.