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:
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.