Separate chunks of material so it renders as two lists not one loose list

lessons/R-complex-time-series-models-1/r_tutorial.qmd

@@ -142,6 +142,8 @@ mcmc_plot(baseline_model, type = "trace", variable = c("mintemp", "ar1[1]", "sig
 * But part of what's going on here is that we're using a poorly specified model given the data because we've assumed Gaussian errors
 * So let's look at the model & forecast and then keep going
 
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 * We can look at the model structure using `summary()`
 
 ```r
@@ -196,10 +198,14 @@ hist(rpois(n = 1000, lambda = 4.5))
 
 * If the mean is 4.5 sometimes you'll draw a 4, sometimes a 5, sometimes a 0 or a 10
 
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 * $\lambda_t$ can be a decimal
 * We could expect an average of 4.5 rodents based on the environment even though we can only observe an integer number
 * But $\lambda_t$ it does have to be positive because we can't reasonably expect to see negative rodents
 
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 * To handle this we use a log link function to give us only positive values of $\lambda_t$
 * The log link means that instead of modeling $\lambda_t$ directly we model $log(\lambda_t)$
 
@@ -226,6 +232,8 @@ plot(poisson_model)
 
 * Model structure looks OK, be we still have some residual seasonal lag we haven't captured
 
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 * Now let's look at the forecast
 
 ```r
@@ -296,6 +304,8 @@ plot_predictions(poisson_gam_model, condition = "mintemp")
 * Abundance then increases with temperature
 * But starts to asymptote at higher temperatures
 
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 * How does this influence the forecasts
 
 ```r

lessons/R-complex-time-series-models-2/r_tutorial.qmd

@@ -142,6 +142,8 @@ mcmc_plot(baseline_model, type = "trace", variable = c("mintemp", "ar1[1]", "sig
 * But part of what's going on here is that we're using a poorly specified model given the data because we've assumed Gaussian errors
 * So let's look at the model & forecast and then keep going
 
+<!-- -->
+
 * We can look at the model structure using `summary()`
 
 ```r
@@ -196,10 +198,14 @@ hist(rpois(n = 1000, lambda = 4.5))
 
 * If the mean is 4.5 sometimes you'll draw a 4, sometimes a 5, sometimes a 0 or a 10
 
+<!-- -->
+
 * $\lambda_t$ can be a decimal
 * We could expect an average of 4.5 rodents based on the environment even though we can only observe an integer number
 * But $\lambda_t$ it does have to be positive because we can't reasonably expect to see negative rodents
 
+<!-- -->
+
 * To handle this we use a log link function to give us only positive values of $\lambda_t$
 * The log link means that instead of modeling $\lambda_t$ directly we model $log(\lambda_t)$
 
@@ -226,6 +232,8 @@ plot(poisson_model)
 
 * Model structure looks OK, be we still have some residual seasonal lag we haven't captured
 
+<!-- -->
+
 * Now let's look at the forecast
 
 ```r
@@ -296,6 +304,8 @@ plot_predictions(poisson_gam_model, condition = "mintemp")
 * Abundance then increases with temperature
 * But starts to asymptote at higher temperatures
 
+<!-- -->
+
 * How does this influence the forecasts
 
 ```r

lessons/R-evaluating-forecasts-2/r_tutorial.qmd

@@ -112,6 +112,8 @@ length(in_interval[in_interval == TRUE]) / length(in_interval)
 * Instead of evaluating the mean prediction (point forecast) evaluate the prediction interval
 * _Add two sets of intervals on the axes_
 
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 * Winkler Score
 * Width of the prediction interval + a penalty for points outside the interval
 
@@ -142,6 +144,8 @@ accuracy(forecasts, test, list(winkler = winkler_score), level = 80)
 * _Add a distribution to the axes with the mode matching $\hat{y}$_
 * The best models most closely match the empirical distribution
 
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 * Doing this is technically complicated
 * Continuous Rank Probability Score
 * Scores each value relative to the predicted cumulative distribution function

lessons/R-evaluating-forecasts/r_tutorial.qmd

@@ -68,6 +68,8 @@ glance(portal_models)
 * We know we don't have this for TSLM, so it's likelihood and IC values are invalid
 * These comparisons also typically tell us about 1 step ahead forecasts and we may care about more steps
 
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 * So it's best to evaluate forecasts themselves
 * Ideally we make a forecast for the future, collect new data, and then see how well the forecast performed
 * This is the gold standard, but it requires waiting for time to pass
@@ -171,6 +173,8 @@ $$RMSE = \sqrt{mean[(y_{t+h} - \hat{y}_{t+h})^2]}$$
 
 * Which gives us a measure of the average error in the units of the response variable
 
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 * `accuracy` function shows a number of common measures of forecast accuracy
   * 1st argument: forecast object from model on training data
   * 2nd argument: test data time-series

lessons/R-intro-to-forecasting/r_tutorial.qmd

@@ -92,6 +92,8 @@ ar1_forecast
   * The expected value, or point forecast, is in `$.mean`
   * And information about the error term in `abundance <dist>`
 
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 * Change the number of time-steps in the forecast using h (default to 2 seasonal cycles)
 
 ```r
@@ -140,6 +142,9 @@ autoplot(ar1_forecast, pp_data)
 
 * This lets us run a single forecast including a randomly chosen value for $epsilon_t$ at each time step
 * Let's run it a few times
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 * Quantify variability of forecast outcomes
 * If we set `times` to `1000`
 
@@ -152,6 +157,9 @@ autoplot(ar1_forecast, pp_data)
 * Shaded areas provides uncertainty
 * These are the "prediction intervals"
 * The region within which some percentage of our 1000 forecast values occurred
+
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 * For many models the values can be calculated without making separate forecasts
 * This is the default behavior that we first saw
 
@@ -186,6 +194,9 @@ $$y_t = c + \beta_1 x_{1,t} + \epsilon_t$$
 
 * So we need values of $x_{1,t}$ to make predictions for time step $t$
 * To forecast with covariates we need forecasts for those covariates
+
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 * Since our time-series ended in 2020 we'll use the observed values for the next two years
 
 ```r

lessons/R-species-distribution-models/r_tutorial.qmd

@@ -41,6 +41,8 @@ library(terra)
 * Fore forecasts of environmental data we'll use CMIP5 50 year forecasts (CMIP = coupled model intercomparison project)
 * Download data from [https://course.naturecast.org/data/sdm_data.zip](https://course.naturecast.org/data/sdm_data.zip) and unzip it into your working directory
 
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 * The hooded warbler data is in a csv file
 * Load it using `read.csv()`
 
@@ -51,6 +53,8 @@ head(hooded_warb_data)
 
 * We can see that this file has information on locations as latitude & longitude plus whether or not the species is present at that location
 
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 * The environmental data is stored in raster stacks in `.grd` files
 * Load those using the `rast()`, which is part of the `terra` package
 
@@ -153,6 +157,8 @@ points(present_loc, pch='+', cex = 0.5)
 * The 1:1 line on this graph is what we would get if we randomly assigned each point to be present or absent
 * So we definitely want a model that is above that line
 
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 * Let's make our own ROC curve
 * Split the data in into presences and absences
 

lessons/R-state-space-models-1/r_tutorial.qmd

@@ -189,6 +189,8 @@ plot(time, predictions, type = "l")
 
 * And this looks very similar to the observed dynamics of y
 
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 * Add prediction intervals as range containing 95% of MCMC samples
 
 ```

lessons/R-state-space-models-1/r_tutorial_mvgam.qmd

@@ -310,6 +310,8 @@ plot(time, predictions, type = "l")
 
 * And this looks very similar to the observed dynamics of y
 
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 * Add prediction intervals as range containing 95% of MCMC samples
 
 ```

lessons/R-state-space-models-2/r_tutorial.qmd

@@ -27,6 +27,8 @@ excellent
 * This means that this type of modeling approach also works naturally with missing data
 * This is different from many types of time-series models that require continuously sampled time-series
 
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 * To illustrate this we'll add `NA`'s to a portion of our time series as an example of missing data
 * Go back to the line where we replaced the end of the time-series with `NA`'s and add some `NA`'s inside the training portion of the data
 * We'll use two examples of missing data

lessons/R-time-series-data/material.qmd

@@ -10,4 +10,6 @@ order: 1
     * [NEON_HarvardForest_date.csv](/data/NEON_Harvardforest_date_2001_2006.csv)
     * [NEON_HarvardForest_datetime.csv](/data/NEON_Harvardforest_datetime.csv)
 
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 * R_tutorial videos and written notes available through R tutorial link.

lessons/R-time-series-modeling-2/r_tutorial.qmd

@@ -46,6 +46,8 @@ data_ts
 * Greenness isn't really driven by greenness in the same way a populations abundance is
 * But if it's greener than normal this month it's probably a good year so it's likely to be greener than normal next month
 
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 * Both AR and MA structures can be present in time-series
 * We can combine them in an ARMA model
 
@@ -63,6 +65,8 @@ data_ts
 
 * So, if we difference the data we are now modeling the change from time-step to time-step, not the actual values
 
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 * Adding AR, MA, and differencing together gives us an ARIMA model
   * AR: Autoregressive - Uses past values to predict future values
   * I: Integrated - Uses differencing to handle trends
@@ -93,6 +97,8 @@ report(arima_model)
 * So, if NDVI was above average over the last 3 months we expect it to be above average now
 * This lines up with our idea that MA might be better for NDVI since it indicates a good year
 
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 * But what is the `sar1` coefficient?
 * That's our season signal
 * A seasonal autoregressive term of order 1

lessons/R-time-series-modeling-3/r_tutorial.qmd

@@ -91,6 +91,8 @@ gg_tsresiduals(tslm_model)
 * This ramp suggests that there might be a trend
 * It's possible we have a decrease over time
 
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 * We can try to model the trend explicitly to remove the autocorrelation
 * We can do this by adding a fitted trend to our model using `trend()`
 
@@ -186,6 +188,8 @@ gg_tsresiduals(arima_exog_model)
 * Look at the report, is this model better than the model with just mintemp?
 * What does that tell us?
 
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 * But did you notice anything else weird?
 * Negative abundances don't make sense
 * Why do we have them?

lessons/R-time-series-modeling/r_tutorial.qmd

@@ -163,11 +163,15 @@ gg_tsdisplay(data_ts, NDVI)
 * b_1 is a coefficient determining how y_t is related to y at a 1 time-step lag, i.e., the previous time step
 * e_t is normally distributed error
 
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 * Does this model remind you of a biological model?
 * This model is basically a Gompertz population model if y is log(N)
 * The idea is that the current value influences the future values
 * Makes a lot of sense for things like population dynamics
 
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 * Since we have also have lag 2 autocorrelation we add a term for two time steps back
 
 > `y_t = c + b1 * y_t-1 + b2 * y_t-2 + e_t, where e_t ~ N(0, sigma)`

lessons/election-forecasts/discussion_questions.qmd

@@ -8,6 +8,8 @@ order: 2
 * What dot he simulations tell us?
 * How does this approach compare to that used for hurricane forecasting? What are the similarities and differences?
 
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 * What is the main difference between 538's approach and MRP?
 * What data does it use and what are the sources of uncertainty related to it?
 * Why does the author argue that this method pointing in the same direction as other methods should strengthen the overall strength of our predictions?

lessons/intro-time-series-data/instructor_notes.qmd

@@ -19,10 +19,14 @@ order: 4
         * Resurvey -> Idiosyncratic -> Continuous w/Gaps -> Continuous
         * Place purely spatial data off on one end the side with a "spatial only" label.
 
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 * Ask what types of data are easier/harder to collect
 * Ask what types are more common for going further back in time vs. more recent
 * (optionally) Draw these gradients on board
 
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 * How long do you think most ecological studies/time-series are?
 * Show: Recent study by Estes et al. 2018
 

lessons/paleo-dynamics/material.qmd

@@ -5,4 +5,6 @@ order: 1
 
 * Reading: Just the Introduction of [Ecological Change, Range Fluctuations and Population Dynamics during the Pleistocene](https://doi.org/10.1016/j.cub.2009.06.030) (i.e. stop when you reach the section titled "The Glacial Refugium Theory")
 
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 * Reading: Read all of [Novel climates, no-analog communities, and ecological surprises](https://doi.org/10.1890/070037)

lessons/uncertainty-dietze-ch-2/instructor_notes.qmd

@@ -46,6 +46,8 @@ order: 4
 * How does disturbance make forecasting difficult?
   * What could be done to ameliorate the influence of disturbance on forecasts?
 
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 * Which components of uncertainty (e.g., in eq. 2.1) have the potential to grow
   through time?
   * What implications does this have for our ability to forecast?
@@ -57,6 +59,8 @@ order: 4
 * What are the implications for forecasting?
 * How can we tell them apart?
 
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 * What kinds of uncertainty/variability do you think are most important in
   ecological systems?
 * If a forecast model doesn't include all of these sources of variance can it be