Sentences with phrase «of calibration curve»

Note that for this computation it is not necessary to know the slope of the calibration curve at calendar age 1000.

The prior gives virtually zero probability to large intervals of calendar age based solely on the shape of the calibration curve, with this curve being the result of physical processes that almost certainly have nothing to do with the age of the sample.

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.

Initially I was concerned that the non-monotonicity problem was exacerbated by the existence of calibration curve error, which results in uncertainty in the derivative of 14C age with respect to calendar age and hence in Jeffreys» prior.

Now we'll take the 1000 — 1100 years range, which asymmetrically covers a steep region in between two plateaus of the 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.

Any confidence interval obtained from the Jeffrey's prior model will certainly either have the flat part of the calibration curve IN or OUT.

However, I'm not convinced that his treatment of calibration curve uncertainty is noninformative even in the absence of it varying with calendar age.

The key point here is that the objective Bayesian and the SRLR methods both provide exact probability matching whatever the true calendar date of the sample is (provided it is not near the end of the calibration curve).

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.

The statistical relationship then becomes, given independence of calibration curve and radiocarbon determination uncertainty:

Subjective Bayesians will probably throw up their hands in horror at it, since it would be unphysical to think that the probability of a sample having any particular calendar age depended on the shape of the calibration curve.

I have accordingly carried out frequentist coverage testing, using 10,000 samples drawn at random uniformly from both the full extent of my calibration curve and from various sub-regions of it.

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.

«We could use the calibration curve that we describe in the second paper to predict the length of time it will take the material to crystallise.»

This allowed absolute quantitation to be achieved with an external calibration curve generated from standards containing the same fixed concentration of propranolol - d7 and varied concentrations of propranolol.

Calibration curves correlating this ratio to the total expression time can therefore be used to determine how long a pool of FP timers has been expressed, either in whole cells or as a pool of fusion proteins localized to a specific region of the cell.

Results from each aliquot were plotted by the software onto a simultaneously run calibration curve generated from known quantities of DYS14.

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.

the Oxygen isotopic curves, and to assess the calibrations of 40Ar39Ar.

Rear - wheel steering remains for the vastly improved agility that it brings, but with a completely different calibration of the response curve.

Intensive testing and calibration of the power - assist curve ensures the steering feel matches handling characteristics.

If we calibrate a driver / response relationship based on a criterion of some minimal correlation (or probability) from a linear model, but the calibration period from which that derives only actually samples some part of a more complex, non-linear response surface / curve, then the estimates of the parameter of interest in times past could be seriously wrong and / or the certainty in the parameter over-estimated.

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.

And this portion of the reconstruction curve still contains higher frequency data than is present outside of the calibration period.

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.

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.

In short, we saw from Keenan's intuitive description that if the calibration curve were ideal, the grey cake would implode in the middle.What the precise effect of the blue sausage is on the grey cake remains a puzzle.

I think in this respect the Keenan paper must make some fault as the calibration curve uncertainty must be of the same order in size there as the measurement error.

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.

However, I am in agreement regarding the technical details and calculations you give, with one exception — after showing that the subjective Bayesian credible interval based on the posterior CDF has perfect probability matching when the parameter value is randomly chosen from the subjective prior that is used, you remark that this is «probably reflecting the near symmetrical form of the stylised overall calibration curve».

In order to make the problem analytically tractable and the performance of different methods — in terms of probability matching — easily testable, I have created a stylised calibration curve.

The context of our carbon dating here already largely fixes the measures: There is one on the C14 age dating and one on the calibration curve.

The calibration curve is derived by taking samples from objects of known reliable calendar date and calculating the RC age on those samples (using the same assumed initial mass fraction as in our sample measurement).

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.

I've assumed an error standard deviation of 30 14C years, to include calibration curve uncertainty as well as that in the 14C determination.

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.

And it's then an integral over the data space, not the parameter space, and the width of the interval integrated over is fixed by the rounding process, not affected by the calibration curve.

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.

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.

Figure 2 shows similar information to Figure 1 but with my stylised calibration curve instead of a real one.

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.

The curve carries a standard deviation of 1000 hours, say, from the calibration tests.