The goal of braggR is to provide easy access to the
revealed aggregator proposed in Satopää
(2021).
You can install the released version of braggR from CRAN with:
install.packages("braggR")This section illustrates braggR on Scenario B in Satopää
(2021).
library(braggR)
# Forecasters' probability predictions:
p = c(1/2, 5/16, 1/8, 1/4, 1/2)
## Aggregate with a fixed common prior of 0.5.
# Sample the posterior distribution:
post_sample = sample_aggregator(p, p0 = 0.5, num_sample = 10^6, seed = 1)
# The posterior means of the model parameters:
colMeans(post_sample[,-1])
#> rho gamma delta p0
#> 0.3821977 0.4742795 0.6561926 0.5000000
# The posterior mean of the level of rational disagreement:
mean(post_sample[,3]-post_sample[,2])
#> [1] 0.09208173
# The posterior mean of the level of irrational disagreement:
mean(post_sample[,4]-post_sample[,3])
#> [1] 0.1819131
# The revealed aggregator (a.k.a., the posterior mean of the oracle aggregator):
mean(post_sample[,1])
#> [1] 0.1405172
# The 95% credible interval of the oracle aggregator:
quantile(post_sample[,1], c(0.025, 0.975))
#> 2.5% 97.5%
#> 0.001800206 0.284216903This illustration aggregates the predictions in p by
sampling the posterior distribution 1,000,000 times. The
common prior is fixed to p0 = 0.5. By default, the level of
burnin and thinning have been set to num_sample/2 and
1, respectively. Therefore, in this case, out of the
1,000,000 initially sampled values, the first
500,000 are discarded for burnin. Given that thinning is
equal to 1, no more draws are discarded. The final output
post_sample then holds 500,000draws for the
aggregate and the model parameters, rho,
gamma, delta, and p0. Given that
p0 was fixed to 0.5, it is not sampled in this
case. Therefore all values in the final column of
post_sample are equal to 0.5. The other
quantities, however, show posterior variability and can be summarized
with the posterior mean. The first column of post_sample
represents the posterior sample of the oracle aggregator. The average of
these values is called the revealed aggregator in Satopää
(2021). The final line shows the 95% credible interval
of the oracle aggregator.
# Aggregate based on a prior beta(2,1) distribution on the common prior.
# Recall that Beta(1,1) corresponds to the uniform distribution.
# Beta(2,1) has mean alpha / (alpha + beta) = 2/3 and
# variance alpha * beta / ((alpha+beta)^2*(alpha+beta+1)) = 1/18
# Sample the posterior distribution:
post_sample = sample_aggregator(p, alpha = 2, beta = 1, num_sample = 10^6, seed = 1)
# The posterior means of the oracle aggregator and the model parameters:
colMeans(post_sample)
#> aggregate rho gamma delta p0
#> 0.1724935 0.5636953 0.6376554 0.9892552 0.6662238This repeats the first illustration but, instead of fixing
p0 to 0.5, the common prior is now sampled
from a beta(2,1) distribution. As a result, the final
column of post_sample shows posterior variability and
averages to a value close to the prior mean 2/3.