Bayesian statistics is a growing field of exploring
data-rich, complicated, explanation-poor phenomena. In a nutshell, you start
out with an initial assumption, called a “prior” and then modify it with new
sets of independent data. The Bayesian approach is one of the hot new
techniques to come into Earth Science in the past decade, as it allows us to
sensibly integrate disparate sets of data about the same physical process
derived from different proxies or fields. Long time geobloggers will know that
James is an expert in applying this technique to climate; see his blog and
papers for more information. However,
despite the decade-long use in climate science, Bayesian statistics have not
often been applied to more interesting areas of geoscience. E.g. Geochronology. Until now.
In Geology, Vleeschouwer & Parnell present a new
Bayesian method of constructing the geologic timescale. They point out that the previous timescale,
which were just spline fits between selected stratigraphic/geochronological
time points, had the perverse effect of yielding smaller error bars in the gaps
between data points than near to where there are data. So they try a Bayesian
approach instead.
For their Prior, they start off with the rule of
superposition- which states that lower stratigraphy is older than higher
stratigraphy. They then apply all the
high precision geochronology dates (high-precision CA-TIMS U-Pb in this case),
and generate a probability density function for stratigraphy vs time. Their resulting
chronology is, sensibly, more erroneous in areas where there is no data,
compared to those where data does exist.
But in addition to being more sensible, this approach is far more
useful.
Firstly, from the modeled uncertainties in the interpolated
regions, one can guestimate the precision (both geochronological and
stratigraphic) that is necessary to help constrain the timescale. So, for example, in some of the more
data-poor regions, one can probably usefully constrain the timescale using a
less precise microanalytical method such as SHRIMP, if the only available
zircons are not suitable for CA-TIMS. On
the other hand, as you approach a high precision date, lower precision
techniques become less useful.
In fact, you can tell whether or not a particular age is
useful for the timescale simply by looking at how the inclusion of that date
alters the PDF. Previously, the
inclusion or rejection of particular ages has been a non-transparent
potentially politicized process. The use
of this model allows us to replace the argumentative old men with statistics.
Of course, one needs to be careful in adding data. A potential flaw would be adding lots of data
with a systematic error (for example, of there are still lingering systematic
issues with U-Pb vs Ar-Ar dating, or the offsets in some zircon ages dated
using laserICP by Gehrels et al. 2008). But one thing this method does allow is
the addition of different types of data.
Vleeschouwer and Parnell (2014) demonstrate this in the second half
of their paper, using astrochronology.
This is the appearance in the sedimentary record of depositional changes
that are related to Milankovic cycles- the changes in the Earth’s orbit that
govern, for example, the extent of ice sheets in the modern Earth. Astrochronology cycles do not add additional
tie points to the geochron/stratigraphy tie curve, as they are relative dates
with no fixed reference. However, what
they can do is constrain the slope of the line.
So changes in stratigraphic distance between periodic eccentricity cycles
tells us how the stratigraphic progression changes with time, often on a much
shorter timescale than what we can access using traditional U-Pb geochronology. The Bayesian approach allows us to integrate
the strengths of both methods, giving a more accurate and reliable timescale.
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