Short Introduction to BAMP

Data example

BAMP includes a data example.

data(apc)
plot(cases[,1],type="l",ylim=range(cases), ylab="cases", xlab="year", main="cases per age group")
for (i in 2:8)lines(cases[,i], col=i)

APC model with random walk first order prior

model1 <- bamp(cases, population, age="rw1", period="rw1", cohort="rw1",
              periods_per_agegroup = 5)

bamp() automatically performs a check for MCMC convergence using Gelman and Rubin’s convergence diagnostic. We can manually check the convergence again:

checkConvergence(model1)

## [1] TRUE

Now we have a look at the model results. This includes estimates of smoothing parameters and deviance and DIC:

print(model1)

## 
##  Model:
## age (rw1)  - period (rw1)  - cohort (rw1) model
## Deviance:     231.46
## pD:            36.95
## DIC:          268.40
## 
## 
##  Hyper parameters:                 5%           50%          95%         
## age                              0.391        1.050        2.277
## period                          65.550      194.839      615.902
## cohort                          35.000       59.443       98.255

We can plot the main APC effects using point-wise quantiles:

plot(model1)

More quantiles are possible:

plot(model1, quantiles = c(0.025,0.1,0.5,0.9,0.975))

Prediction

Using the prior assumption of a random walk for the period and cohort effect, one can predict cases for upcoming years.

pred <- predict_apc(object=model1, periods=3)

m<-max(pred$pr[2,,])
plot(pred$pr[2,,8],type="l", ylab="probability", xlab="year", ylim=c(0,m))
for (i in 7:1)
  lines(pred$pr[2,,i],col=8-i)
legend(1,m,col=8:1,legend=paste("Age group",1:8),lwd=2,cex=0.6)
lines(c(10.5,10.5),c(0,1),lty=2)