Making predictions

David L Miller

So far...

Build, check & select models for detectability
Build, check & select models for abundance
Make some ecological inference about smooths
what about predictions

What predictions do we want to make?

Abundance estimates
Maps of abundance
These are related

Let's talk about maps

What does a map mean?

Grids!
Each cell is an abundance estimate
Whole map is a “snapshot”
Sum all the cells to get the overall abundance
Sum a subset to get a stratified estimate

Going back to the formula

Model: \[ n_j = A_j\hat{p}_j \exp\left[ \beta_0 + s(\text{y}_j) + s(\text{Depth}_j) \right] + \epsilon_j \]

Predictions (index \( r \)): \[ n_r = A_r \exp\left[ \beta_0 + s(\text{y}_r) + s(\text{Depth}_r) \right] \]

Need to “fill-in” values for \( A_r \), \( \text{y}_r \) and \( \text{Depth}_r \).

Predicting

With these values can use predict in R
predict(model, newdata=data)

Rasters

Jason has talked about rasters a bit
In R, the data.frame is king
Fortunately as.data.frame exists
Make our “stack” and then convert to data.frame

Prediction data

           x      y      Depth       SST      NPP off.set
126 547984.6 788254  153.59825  9.049170 1462.521   1e+08
127 557984.6 788254  552.31067  9.413981 1465.410   1e+08
258 527984.6 778254   96.81992  9.699239 1429.432   1e+08
259 537984.6 778254  138.23763  9.727216 1424.862   1e+08
260 547984.6 778254  505.14386  9.880866 1379.351   1e+08
261 557984.6 778254 1317.59521 10.091471 1348.544   1e+08

Predictors

plot of chunk preddata-plot

Making a prediction

Add another column to the prediction data
Plotting then easier (in R)

predgrid$Nhat_tw <- predict(dsm_all_tw_rm, predgrid)

Maps of predictions

plot of chunk predmap

p <- ggplot(predgrid) +
      geom_tile(aes(x=x,y=y,fill=Nhat_tw)) +
      scale_fill_viridis() +
      coord_equal()
print(p)

Total abundance

Each cell has an abundance, sum to get total

sum(predict(dsm_all_tw_rm, predgrid))

[1] 2491.864

Subsetting

R subsetting lets you calculate “interesting” estimates:

# how many sperm whales at depths less than 2500m?
sum(predgrid$Nhat_tw[predgrid$Depth <= 2500])

[1] 1006.271

# how many sperm whales North of 0?
sum(predgrid$Nhat_tw[predgrid$x>0])

[1] 1383.744

Extrapolation

DANGER WILL ROBINSON, DANGER

What do we mean by extrapolation?

Predicting at values outside those observed
What does “outside” mean?
Multidimensional problem

"Outside"

plot of chunk out

Temporal extrapolation

Models are temporally implicit (mostly)
Dynamic variables change seasonally
Migration can be an issue
Need to understand what the predictions are

Extrapolation

Extrapolation is fraught with issues
In general, try not to do it!
Want to be predicting “inside the rug”
More on this in the “advanced” lecture

Recap

Using predict
Getting “overall” abundance
Subsetting
Plotting in R
Extrapolation (and its dangers)