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"