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Expert Elicitation
So, expert elicitation is a pretty powerful process. It’s a rigorous approach to be able to systematically describe relationships, whether those are probability distributions, or connections between various variables that we expect, and really make our scientific knowledge transparent. It’s been used in a number of cases where there simply is not data and information to be able to make assessments, but experts have knowledge that needs to be included in decisions, so, for example, some pretty famous examples of very rigorous expert elicitations being employed related to choosing between different locations for where you could store nuclear waste in the United States.
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Machine Learning
I’m Barbara A. Han, I’m a disease ecologist at the Cary Institute, I work with Shannon and Kathy who are just down the hall from me. Mike asked me to talk to you guys today about machine learning which seems like a really daunting field or area to talk about so, I’m gonna try to give sort of a broad overview and really connect it more towards the type of datasets and questions that we might ask as ecologists and I’m gonna use some examples from work that I do from my program looking at infectious diseases.
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Data Assimilation: Analytical Methods
So where I wanna start this afternoon, and then continue tomorrow morning, is the discussion of what’s referred to as data simulation. I think I mentioned on the first day that the first data simulation meeting for ecologists I went to, spent most of the three days arguing about what ecologists meant by data simulation, but in the physical environmental sciences there’s a very specific meaning which is this process of iteratively updating models as new information becomes available, which is different than calibration, which is constraining your model’s parameters with data.
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Trade-offs, Value of Information, Adaptive Management, & Decision Support Communication
We are going to go whirlwind-through some examples with this PrOACT approach. We’re gonna talk about three different methods to assess decision trade-offs, cost benefit analysis, dominance methods, and multi-attribute criteria analysis, or multi-attribute utility analysis. We won’t be able to get into a lot of the details and weeds, but there’s a couple references at the end and that structure and decision making book I think is a really great one for being able to look at some of these approaches.
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Characterizing Uncertainty
I’m gonna talk about characterizing uncertainty, in a kind of a broad sense, but really only broad within a destination of why you wanna use Bayesian statistics. We have some classic assumptions, whenever we’re learning about statistics throughout much of our training, and for many people still probably whenever you’re doing a statistical inference. Homoscedasticity, so our variance is constant across time. The X variables, and X being the predictor variables, are in fact not variables, right?
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Propagating Uncertainty
Like I said, we spent a good bit of the last day and a half after the general introduction, really focused on statistical tools that solve what is ultimately the calibration problem. We have some model, we have some data, we need to estimate the parameters to that model. We covered some fairly sophisticated ways of doing that. Methods for dealing with the complexity of data, observation errors, errors and variables, non-constant variance, blah, blah, blah, non-Gaussian distributions, we talked about using hierarchal models to partition that variability, we talked about using state-space models to fit these as dynamic time series, but they were all ultimately about calibration, about fitting that model.
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State Space Models
So State Space Models. So again, to remind you of the kind of inferential world we’ve been in, we generally think about modeling statistics as kind of signal versus noise, and we have some model of that signal. And in this case, you know, a linear model with some kind of slope and intercept. And we put biological or ecological relevance on those parameters, oftentimes that we want to assign signal to.
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Why Forecast?
There was a nice Tweet from Ethan White slab last week I think, where he got a review back saying, “This is all great, “but why should we forecast as ecologists? “Why bother?” So I wanna give a perspective on why we should bother and why particularly, I think iterative forecasting is an important direction for ecology to go. So as Moses said, decisions are fundamentally about the future.
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Bayesian Hierarchical Models
Hierarchical Bayes, so what I kinda wanna do here, is build on what Shannon talked about yesterday afternoon; which I think really laid the foundation for, in my mind, the idea that ecological data are complex. They have a lot of idiosyncrasies, and it’s important for us to bring appropriate statistical tools to deal with that complexity of data. Often construct models individualistically for specific types of analysis based on the characteristics of those data and their challenges, rather than taking data and trying to twist them sometimes inappropriately to fit some long-standing canned test; the classic ones we learned, an interest that’s what derived, quite a while ago, at a time when we couldn’t solve problems computationally.
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Data Assimilation: Ensemble Methods
So this is the second lecture on data assimilation methods and the one where I want to introduce numerical methods for doing data assimilation. And so this pairs very nicely with again the lesson on uncertainty propagation where in that lecture we discovered analytical methods for propagating uncertainty, linear tangent approach, the exact transformation of the distribution and the analytical approach to transforming moments. And we saw when I introduced the analytical approaches to data assimilation yesterday, that we could map the analytical approach to uncertainty propagation to the Kalman Filter and the linear tangent approach to the Extended Kalman Filter.