In the endless and unrewarding debate about global warming, a scientific fellow assured me that new computer models could handle "boundary conditions" which made its climate modeling much more accurate.
Sorry, we are not dealing with math or statistics that I don't know.
All climate models are....
All climate models are based on solving a set of simultaneous equations. Regardless of the number of variables or the consequent number of equations, the equations are just homely theoretical relationships built on seat of the pants analysis from original regressions applied to the raw climate data.
A regression model is a statistical device. Like nearly all statistics it is based on one simple mathematical operation: the average. All my readers know what an average is. The sum of a1+a2+a3 divided by 3 is the core of all mathematical analysis. Averages can be based on squares, least squares, differences, exponents or any other number manipulator but it still ends up being an average.
I don't want to over generalize about the universal power of an average. There are several analytic forms that allow elegant transformation of data directly to a recognizable form such as Fourier transforms or multi-dimensional scaling. We must keep in mind that these are irrelevant for prediction and modelling; they are highly appropriate for specific experiments.
In drawers and windowless rooms, we have reams of climate data over long periods of time. When we put it together we are always using averages subjected to a wide array of statistical distortions trying to make the raw numbers, from those windowless rooms, useful for analysis. We then create a mini-theory to connect the averages and build a model that connects all the mini-theories into a grand theory.
Hype, new computers and arrogance don't change the basic processes for analyzing data, the kind that I have worked with for nearly fifty years.
Sorry folks, nothing new has happened since I last worked in statistics a few weeks ago. I know how rotten data and technical manipulation can be. Climate change, global warming remain pure hysteria, not subject to rational discussion or intelligent insight.