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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