Final Exam: STA465/ STA2016
The final exam is due on Friday, April 23rd at 11:59 p.m. EST. The final exam is worth 20 points in total.
Fitting Models
Fit the following five models to the malaria prevalence in The Gambia data set in INLA using the default
priors + penalized complexity priors for those models that include the spatial random eect (a total of 7
models):
Complete pooling and altitude (no random eects)
Hierarchical random eect (iid) – (intercept only)
Hierarchical random eect (iid) + altitude covariate
Spatial + iid random eect
Spatial + iid random eect + altitude covariate
Include all INLA code. For each model, compute the CPO, PIT values and create maps of mean predicted
prevalence along with upper and lower limits of predicted prevalence. These maps should include predictions
of prevalence across the entire country (as has been done in Homework 4). Comment on any major dierences
in predicted prevalence across models. Explain y
our choice of penalized complexity prior.
Spatial Residuals
For each model, compute (observed prevalence – mean predicted prevalence) and plot these values (on a
map). There should be a total of 7 maps. Comment on any patterns you observe in and across the maps.
For models that do not include a spatial component, are there any patterns you observe that would indicate
the need for a spatial random eects term
Results + PIT histograms
Organize the results of the estimates, 95% credible intervals, sum log(CPO) for each model in a table. Plot
a histogram of the PIT values. Which model has the best predictive performance as measured by sum
log(CPO) Should we be concerned if we select a ‘best predictive performance’ model via CPO
Spatial K-fold CV
Measure the predictive capacity of each model via a 4-fold CV that takes spatial dependence into account.
Include all R and INLA code.
Make a map that shows how the data are partitioned into the 4 folds.
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