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 0.284216903
This 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
500,000
draws 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 0.6662238
This 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
.
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