Bayesian Stats 1

Grid approximation

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Create probability vector

p <- seq(from = 0, to = 1, length.out = 1000)
plot(p)

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Create prior vector

prior <- rep(1, 1000)
plot(prior)

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Create likelihood vector

likelihood <- dbinom(6, size = 9, prob = p)
plot(likelihood)

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Create posterior vector

posterior <- prior * likelihood
posterior <- posterior / sum(posterior)
plot(p,posterior)

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Sample p using posterior vector as distribution

samples <- sample(p, prob = posterior, size = 1e4, replace = TRUE)
plot(samples, type = "p", col= "#99ccff")
plot(density(samples))

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Calculate area under curve interval 0-50%

x1 = 1
x2 = 500
sum(posterior[p<0.5])

[1] 0.1718746

with(plot(p,posterior), polygon(x = c(0, p[x1:x2], p[x2]), y = c(0, posterior[x1:x2], 0), col="skyblue"))

x1 <- min(which(density(samples)$x >= 0))  
x2 <- max(which(density(samples)$x <  0.5))
sum(samples<0.5)/1e4

[1] 0.1728

with(plot(density(samples)), polygon(x=c(density(samples)$x[c(x1,x1:x2,x2)]), y= c(0, density(samples)$y[x1:x2], 0), col="orange"))