Reflections by One Statistician Jarrett Barber University of Wyoming Department of Statistics

Data Models Assimilation Integration Fusion Assintegrofussatamodeling.

“New” Modeling Framework [Data|process] *[process|parameters]*[parameters] Basic elements –Fundamental probability rules: conditional specification: model locally, infer globally –Process modeling and more empirical (“regression”) expertise –Technical methodologies (MCMC) Nice thing: it’s more plug ‘n’ play Bad thing: it’s more plug ‘n’ play

Issues A Reasonable Perspective: Models (mean or covariance) are wrong. Check your models. (More than ever.) –Model comparisons: information criteria –Observed versus predicted –Many model components. How check? Education –Traditional statistical methods verses probability modeling. –Substantive area expertise (process modeling) –Computational/Mathematical techniques Just the beginning –Need some (new) way to facilitate modeling related activities –“NEON:” More than more data?

Really Big Models When your predictions (forecasts) given by your best model still don’t behave then use data to “adjust” states (i.e., the outputs) by optimal (often linear) prediction: –objective analysis (“Kriging”) –KF and variants –Adjoint method Often not feasible to do do inference for parameters inside the black box because of model complexity (time/computing power limitations). Uncertainty is a problem. –Computer experiments: carefully select a set of parameters at which to run the model and then model the model parameters to find the top of the hill in parameter space.

NEON, etc. More data! And it will be easy to get (once someone figures out how to make it easy). Where/how do models or model components fit here? Do we want more than facilitated data sharing?

Uncertainty/Variability Model framework that promotes explicit accounting of uncertainty/variability while incorporating information in the form of a process (or other) model components –Currently seems to be favoring Bayes E.g., Andrew Latimer charismatic “shrubs” –Priors are important for complex models to behave. Update the priors as we learn.

Data and Users Data: NEON, LTER, P2ERLS, … Assimilators: –Mat Williams, Kelvin Droegemeier, … Integrators –Alan Hastings, Paul Moorcroft, Andrew Latimer, Jizhong (Joe) Zhu, Kiona Ogle, … Modelers –Forward (simulation). Inverse (inference on parameters).

Models Embody theoretical, empirical, phenomenological, semi-mechanistic, mechanistic (mis)understanding of biological phenomenon. –Range of understanding (model components) that go into such models: empirical regression relationships (light response curves) to Big Science fluid flow differential equations. –Forward modeling, parameter “tuning.” –Recent (10-15 years) opportunities for more “formal” parameter estimation and characterization of uncertainty.

Classic Assintegrofussatamodel ModelH Operator Light Response Curves Initial States State Forecast Data Adjusted States