Monday, August 11, 2014
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.