Propagating Uncertainty
Channel: NEON Science
Date: 2020-04-23

In this video in our Ecological Forecasting lecture series, Mike Dietze introduces the key concepts involved in propagating and analyzing uncertainty, so as to produce probabilistic forecasts (a defining feature of what makes a forecast a forecast). This video begins with a quick summary of sensitivity analysis methods, and then build on this to introduce the general trade-offs between different approached in terms of whether they are analytical versus numerical and whether they return a full probability distribution or just moments (e.g. mean and variance). We then goe on to describe the general principles of uncertainty transformations and much simpler analytical ways to calculate moments, which are only exact for linear models. We then use a linear tangent approach to generalize this analytical approach to nonlinear models  We then introduce numerical methods for propagating uncertainty based on Monte Carlo methods that sample from the distribution of inputs/parameters and running the forecast many times, each with unique inputs, to generate a distribution of predictions. When full Monte Carlo methods are too computationally demanding, ensemble methods provide an approximate solution (e.g. means, variances) as the cost of having to make assumptions about probability distributions. We then extend these approaches to explore how we can to partition out the contributions of different uncertainties to our overall predictive uncertainty. Such approaches provide a critical feedback loop from forecasts back to improved measurements and efficient monitoring. We wrap up discussing implications for experimental design, such as power analyzes, optimizing sampling, and observing system simulation experiments.