site so i came to go back the want?.I am trying to find issues to enhance my site!I guess its adequate

to use a few of your ideas!! ]]>

Turney, Briffa, Jones, Hulme and Lewandowsky, too?! What an amazing clamour of voices to add a verse to the “It’s a small, small world” song:

But that aside, Steve, thank you for so many smiles and chuckles … all in one post! If I had to pick one for “quote of the week” it would be a very close tie between your:

Turney appears to have applied the quality control lessons learned at the University of East Anglia to his planning of the Ship of Fools.

and your:

The Turney consortium seems more or less certain that they can get £3.5 million from the NERC; their main stumbling block was that their apparent difficulty in figuring out a coherent rationale for the funding.

The latter of which gives a whole new meaning to the phrase, “Follow the money”, does it not?;-)

]]>Well worth the read.

]]>Extremely helpful information specially the last section :) I maintain such information a lot. I used to be looking for this certain

info for a very long time. Thanks and good luck. ]]>

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. There might be temptation, while devising algorithms, to create new ones, but this has to be very well justified then.

Note I insist on the term “algorithm” because the specifics of the calibration curve requires this.Foremost I think now, it enforces us to handle the “old” C14 age measure half different from the “modern” half. The measure of the old half needs to be preserved no matter what you do with the new half.There is a qualitative difference with with what the calibration curve does, between both halves.

Measure “theory” allows for precise accounting of this.It allows to take these procedural steps.toying around with priors does not do that. The only possibility you have is “take another prior” the last one does not do well.

Can you “fix” it with priors? No doubt you can. there is an infinity of them as well, one probably makes the grey cake look like an elephant with a wiggling trunk.

]]>You obsession with priors, if I may satirize it as such, indicates you have a whole class of solutions in mind, but not all.I agree that that class of solutions has plenty of ambigu pdf’s.

Different pdf’s will be obtained when you re-measure or re-calibrate of course.

So there will always be some ambiguity there, for the end result.

Different algorithms to arrive at the solution will also provide different pdf’s.

But the choice of algorithms is constrained by several factors.

For starters, they have to be correct.

Which means, they should not date a sample of 2700y old like one that is “most likely” 700y old.

This constraint eliminates all of the solutions that use priors, discussed in this post.

As Radford has pointed out, there must be frequency matching on average when the true parameter is drawn from the assumed prior, so long as the math has been done correctly. In my case, that’s a big if, so it’s worth checking whether the two approaches give the same answer. As I’ve pointed out earlier, even an unbounded uniform prior can be drawn from, using an ancillary sampling distribution g(x) and weights 1/g(x).

If the posterior is biased upward or downward or has the wrong scale or skewness for a particular subset of the parameter space, that is a problem only if we can observe what part of the parameter space we are in and so could use that information to improve the posterior. However, we never know for sure what part of the parameter space we are really in, only where the data tells us we are. So if we condition, it must be on where the data tells us we are (using our method, whatever it is), and not on the true parameter values. For this purpose, we could use a point estimate such as the posterior median or mean. (I’d prefer the median in this context, but some might prefer the mean.)

Your Fig. 6 shows that the uniform calendar age prior does terribly when the true calendar age is known to be in the range 1000-1100 years, using your hypothetical calibration curve. What I am asking is, how would it do when say the median estimated posterior calendar age turns out to be in this range? 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.

If my intuition is correct, you should get frequency matching to within Monte Carlo sampling error when you do this. The same should be true if you condition on the mean or any other quantile of the estimated posterior, say the .025 or .975 quantile. Presumably this property of posterior distributions can be shown analytically, but I’ll leave that to someone else!

Of course this test does not tell us that our prior is correct, only that we have used the data efficiently and done the math correctly. Your uniform-in-C14-age prior, or any more specific subjective informative prior should pass the same test. If we knew for sure that the true calendar age was in the range 1000-1100, say, then we should have used that range as our prior. But if we want the data to tell us what the age is, a uniform prior on age that is bounded only at 0 makes sense.

I have another thought I’ll be adding as a comment at the end. ]]>

There is a need for separation of concerns here:

Once Pdf’s are established (measurement of sample and calibration)

we can/must precisely produce an unambiguous pdf of the final result variables.

Unfortunately that’s not possible. There isnt’t any unambiguous way. That’s the whole reason for all this discussion on, how to choose the prior.

Probability/measure theory should be used to obtain these results.

But they do not produce an unambigous result. In some approaches the ambiguity can be put completely in the selection of the measure, in others a measure is fixed first and the ambiguity is in choosing the prior. These approaches are largely equivalent, neither produces unambiguous results, because nothing tells, what’s the right measure out of the infinity of different measures.

That applies also in cases, where the decision has been made to use Jeffreys’ prior. That does not specify fully the situation, because it’s still possible to define the measure in different ways that lead to different priors, all Jeffreys’ priors for that particular measure.

]]>I guess I mean to say that I understand why a uniform grey is chosen now, but our aim should be for more colours. there is middle east (and nowadays also chinese!) pastry shops around that can provide inspiration.. ]]>

It’s indispensable when you do not know what you’re measuring in fact (modeling, like for climate).

In this context however, use of Bayes formula on a quickly scraped together cocktail of numbers from your data (likelihood function) and throwing in some priors , only produces biased results. As we can see. All results are biased in that they suppress old age.

There is a need for separation of concerns here:

Once Pdf’s are established (measurement of sample and calibration)

we can/must precisely produce an unambiguous pdf of the final result variables.

Probability/measure theory should be used to obtain these results.

It is not so much the use/selection of priors in a Bayes formula that will lead to bad results, but rather things like :

-not inducing precisely the probability measures from measurements towards final result variables(eg over a calibration curve).

-not doing convolution integration when errors are added in above step

-not injecting pure randomality where it is needed (eg when your result variable requires that due to non monotonous calibration)and required by probability.

-In a similar vein as above, not respecting the probability constraints that probability measures need to be preserved over respective areas where they are generated, when looked backward at those areas(I refer to the inverse function

which measure theory uses)

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. Clear is that

the grey cake has its left side lobbed off in all instances.There is scant grey paint spent that corresponds to old age pink paint.

I thank you for your attention.

Have a nice day.