365 Days of Climate Awareness 73 - Statistical Inference

A sample, once analyzed descriptively, can then be used to make inferences about the larger population, or environment, the sample was drawn from. There are two main schools of thought in statistical inference. The  first is frequentist, which expands the central limit theorem to the concept that the true average result is the limit of the results of many  trials. Bayesian analytics (named for mathematician Thomas Bayes) holds  that probability exists in a reasonable hypothesis, which can then be modified in light of fresh results. The prior probability, once new evidence is incorporated, is updated to become the posterior probability.

Though in statistical circles frequentist thinking is dominant now, the likelihood of conducting large numbers of trials low outside of computer modeling and laboratory experiment. (Pollsters also follow frequentist models.) Frequentist probability is rigidly quantitative, assigning probabilities to all contributing influences and producing probabilities of future events. Bayesian inference is more  qualitative, relying on a general understanding of events in the worker  to estimate the likelihood of other events.

Climate science involves both. Where repetition is feasible, researchers employ it. But it is often not possible to repeat field investigations often (deep ocean sampling programs come to mind), and an immensely complex system like world climate defies purely quantitative thinking.  While the main parameters such as air temperature, sea surface  temperature, snow cover, ice cover, and precipitation amounts are simple  enough to imagine, gathering them comprehensively through time is a  massive challenge, and the historical records we have are very sparse. Inclusion of this data and estimating the uncertainties to be applied to it are at times subjective decisions.

Predicting future behavior of the climate system is, in one sense, frequentist. Climate models are run thousands of times and compared against each other, and frequently the results are averaged for reports (such as the IPCC's). But the models are tuned, in order to better fit historical trends (a technique called "hindcasting" which we will look at later), and with fresh model results, the assumptions which were built into the model might be modified in order to better match the
historical record. And the process of changing parameters to better fit new information--learning--is central to the Bayesian approach.

Tomorrow: estimates of confidence.

Be well!