# sample_aggregator: Revealed Aggregator In braggR: Calculate the Revealed Aggregator of Probability Predictions

## Description

This function allows the user to compute the revealed aggregator from Satopää, V.A. (2021): Regularized Aggregation of One-off Probability Predictions. The current version of the paper is available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3769945.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```sample_aggregator( p, p0 = NULL, alpha = NULL, beta = NULL, a = 1/2, b = 1/2, num_sample = 1e+06, burnin = num_sample/2, thin = 1, seed = 1 ) ```

## Arguments

 `p` Vector of K ≥ 2 forecasters' probability estimates of a future binary event. These values represent probability predictions and must be strictly between 0 and 1. `p0` The forecasters' common prior. This represents a probability prediction based on some of the forecasters' common evidence and must be strictly between 0 and 1. `alpha, beta` The shape and scale parameters of the prior beta distribution of the common prior. If omitted, the sampler uses the fixed common prior given by `p0`. However, if `alpha` and `beta` are provided, they must be strictly positive. In this case, the common prior `p0` will be treated as a random variable and sampled along with the other model parameters. `a, b` The parameters for the prior distribution of (ρ, γ, δ) in Satopää, V.A. (2021). The default choice `a = 1/2` and `b = 1/2` gives the Jeffreys' independence prior. If p_0 is not equal to 0.5, then `a = 1` and `b = 1/2` give the Jeffreys' prior. `num_sample` The number of posterior samples to be drawn. This does not take into account burnin and thinning. `burnin` The number of the initial `num_sample` posterior draws that are discarded for burnin. This value cannot exceed `num_sample`. `thin` After `burnin` draws have been discarded, the final sample is formed by keeping every `thin`'th value. To ensure that the final sample holds at least two draws, `thin` can be at most `(num_sample-burnin)/2`. `seed` The seed value for random value generation.

## Value

A data frame with rows representing posterior draws of (p*, ρ, γ, δ, p0). The columns are:

• `aggregate`: The posterior samples of the oracle aggregator p*. The average of these values gives the revealed aggregator p''. The 95% interval of these values gives the 95% credible interval of the oracle aggregator.

• `rho`: The posterior samples of the forecasters' shared evidence, ρ.

• `gamma`: The posterior samples of the forecasters' total evidence, γ. The difference `gamma`-`rho` gives the posterior samples of the forecasters' rational disagreement.

• `delta`: The posterior samples of the forecasters' total evidence plus noise, δ. The difference `delta`-`gamma` gives the posterior samples of the forecasters' irrational disagreement.

• `p0`: The posterior samples of the forecasters' common prior. If a beta prior distribution is not specified via the arguments `alpha` and `beta`, then all elements of this column are equal to the fixed common prior given by the `p0` argument.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```# Illustration on Scenario B in Satopää, V.A. (2021). # 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]) # The posterior mean of the oracle aggregator, a.k.a., the revealed aggregator: mean(post_sample[,1]) # The 95% credible interval for the oracle aggregator: quantile(post_sample[,1], c(0.025, 0.975)) # Aggregate based a uniform distribution on the common prior # Recall that Beta(1,1) corresponds to the uniform distribution. # Sample the posterior distribution: post_sample = sample_aggregator(p, alpha = 1, beta = 1, num_sample = 10^6, seed = 1) # The posterior means of the oracle aggregate and the model parameters: colMeans(post_sample) ```

braggR documentation built on May 29, 2021, 5:07 p.m.