Comparing & contrasting Beta priors

The Beta(\(a\),\(b\)) distribution is defined on the interval from 0 to 1, thus provides a natural and flexible prior for your underlying election support, \(p\). You can tune the Beta shape parameters \(a\) and \(b\) to produce alternative prior models. Below you will compare your original Beta(45,55) prior with two alternatives: Beta(1, 1) and Beta(100, 100). The original 10,000 prior_A samples drawn from Beta(45,55) are in your workspace.

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Bayesian Modeling with RJAGS

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Instruções do exercício

Sample 10,000 draws from the Beta(1,1) prior. Assign the output to prior_B.
Sample 10,000 draws from the Beta(100,100) prior. Assign the output to prior_C.
The prior_sim data frame combines the prior_A, prior_B, and prior_C prior samples with a corresponding indicator of the priors. To construct a ggplot() density plot of these 3 separate prior samples on the same frame, specify fill = priors in aes().

Exercício interativo prático

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# Sample 10000 draws from the Beta(1,1) prior
prior_B <- rbeta(n = ___, shape1 = ___, shape2 = ___)    

# Sample 10000 draws from the Beta(100,100) prior
prior_C <- rbeta(n = ___, shape1 = ___, shape2 = ___)

# Combine the results in a single data frame
prior_sim <- data.frame(samples = c(prior_A, prior_B, prior_C),
        priors = rep(c("A","B","C"), each = 10000))

# Plot the 3 priors
ggplot(___, aes(x = ___, fill = ___)) + 
    geom_density(alpha = 0.5)

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