 So, in this video, what I'd like to do is build on what we were talking about in the last few videos in terms of our approaches that we use for propagating uncertainty into forecasts to then think about how we can break down those uncertainties and analyze them in order to better understand our models and our predictions and to hopefully improve them. One of the concepts I'd like to emphasize here is what I call the model data feedback loop. The idea that we might start from observations, use them to calibrate a model, propagate that uncertainty into a prediction and then analyze that uncertainty in terms of breaking them down into the component parts that go in. So I might have a model with multiple parameters and I want to know the contribution of different parameters and processes to my overall prediction. I might have different covariates and I want to understand the contribution of those covariates. You might want to understand the relative importance of parameters versus better constraining the initial condition, the initial current state of the system in terms of how it might reduce the forecast uncertainty. Once I understand how different things impact the forecast uncertainty, that can help me set research priorities that can direct, for example, how I might go and attempt to synthesize our current literature and current data or set up plans for how I might make new measurements that specifically target key sources of uncertainty. One of the things I want to note here is that in ecological systems, most ecologists have an abundance of hypotheses about how all different aspects of our system work. So I don't view this idea of having model data feedbacks prioritizing research as any way in conflicting with the idea of hypothesis-driven research. I think of it more as a way of perhaps prioritizing the order in which we tackle different hypotheses so that we can maximize the information gain and our ability to increase our predictive capacity. To understand how uncertainty analysis works, let's come back to the simple analytical case of being able to propagate uncertainties in terms of the analytical or linear tangent approaches, where in that sense we saw that every component uncertainty could be expressed in terms of the uncertainties in an input, whether that be an initial condition, a parameter, or a driver, and then the sensitivity of the forecast to that prediction. So what we then see is that the overall forecast uncertainty can be decomposed into a sum of the direct impacts of each of these uncertainties and then the interaction terms due to their covariances. This essentially allows us to say what proportion of the predictive uncertainty can be attributed to each of those terms. Furthermore, it allows us to understand when a term contributes a large amount to the predictive uncertainty, is it contributing a large amount because that is an inherently sensitive parameter or process? Or is that contributing a lot because that is a poorly constrained? All else being equal, if we're trying to reduce uncertainties in forecasts, we usually get more bang for our buck by targeting things that are poorly constrained over things that are inherently sensitive, but may already be well constrained. If we take a step back, one of the things that this tells us is that if we want to understand the behavior of our systems and their predictability, we can't do that just with sensitivity analysis alone. This is something that we'll see a lot in the literature is that people use sensitivity analysis to try to understand their models. Because that's only giving us half of the pictures, telling us what's sensitive, but not how that interacts with uncertainties. This flip side, often if we do a calibration exercise, we get an estimate of what's uncertain in our model. So what's the uncertainty in the parameters? That also by itself is insufficient. It's really the interaction between these two things. So if we have parameters that are very sensitive and very uncertain, they're going to contribute a lot to our predictive uncertainty. By contrast, if we have things that are very insensitive and very well constrained, they're going to contribute very little to our predictive uncertainty. And then in between, things can be important either because they're very sensitive or because they're very under constrained. If we look at this more broadly, a complex model to make predictions may have scores of parameters and inputs and initial state variables that we need to put into a model to make a prediction. So as an example, imagine a model had 100 different inputs that needed to go in. All else being equal, we would then expect that on average, each of those things would only contribute 1% to the predictive uncertainty. In practice, it's very rare to see all components of a model contribute equally to the predictive uncertainty. But what we more often see is there's going to be a small number of things that contribute a lot and a larger number of things that contribute a little. That is helpful because it tells us there's a potentially large number of things that are not going to be our priorities. We can kind of take them as given for the time being and really focus our attention on a small number of things that often drive our forecast uncertainty and really prioritize those.