mdsolar's Journal: Mathematical Reticence

(a prediction of more twitter storminess)

Attempting to analyze data leads to a natural parsimony in math. Statistics urges us to limit the number of parameters we use in analysis because using more weakens what we can learn about any one of them. However, it is habitual to work up to first or second order and then stop since the eye and fitting algorithms canâ(TM)t see much more than a curve in typically noisy data. I'm not thinking of data with inherent instrumental profiles but time series in change detection experiments, the -Is something happening?- type question.

An instrumental profile is a priori and deserves a complex treatment. A time series wants to be treated with parsimony. However, the stopping at second order habit becomes reticence of the sort which may impede understanding if there is reason to suspect that an infinite number of orders may be involved. The Taylor expansion of the exponential function, for example, is unending containing terms of unboundedly high order.

In terms of parsimony, it has as many parameters as a second order fit (if you count an offset as a parameter) but it requires nonlinear treatment, fitting in logarithmic space, for example. But in terms of reticence it may seem to the biased to lack in conservatism.

Hansen et al. recently explored the effect of stratification of meltwater water on storminess, sea surface temperature and sea level rise and found that, among other things, their model predicted strong feedbacks in ice sheet exposure to destabilizing influences. Strong feedbacks imply exponential behavior, as even the simplest ordinary differential equation will tell you. Further, their model explained a number of current phenomena and helped explain past instances of very rapid sea level rise and extreme storminess.

Thus, their model predicts the first several meters of sea level rise in the next 50 to 150 years depending on the empirically measured doubling time of ice sheet mass loss. Doubling time is an exponential parameter. That number is not all that well constrained yet thus the range in timescale.

But given that their model works in the past and present, it would be unparsimonious to avoid using an exponential fit to the mass loss data and instead settle for a second order fit that is logically inconsistent with the model. The model cannot predict without the nonlinear treatment.

A pedantic treatment would use a logistics function since we know there is only so much ice sheet mass to be lost. But the early stages of a logistics curve are so close to exponential that their approximation is adequate for the scope of what they are predicting and it is mathematically more parsimonious.

But let us be very clear, it is a prediction just as they state in the abstract, Hillary Clinton partisans and reticently posturing journalists notwithstanding. The work is peer reviewed, and claiming is says other than what it does for political gain is dishonest.