Exercise 4.2 Solution Example - Hoff, A First Course in Bayesian Statistical Methods
標準ベイズ統計学 演習問題 4.2 解答例

using Distributions
using Random
Random.seed!(1234)
y_A = [12, 9, 12, 14, 13, 13, 15, 8, 15, 6]
y_B = [11, 11, 10, 9, 9, 8, 7, 10, 6, 8, 8, 9, 7]

n_A, sy_A = length(y_A) , sum(y_A)
n_B, sy_B = length(y_B) , sum(y_B)

a₀_A = 120
b₀_A = 10
a₀_B = 12
b₀_B = 1

# Posterior distributions
dist_A = Gamma(a₀_A + sy_A, 1/(b₀_A + n_A))
dist_B = Gamma(a₀_B + sy_B, 1/(b₀_B + n_B))

θ_A_mc = rand(dist_A, 5000)
θ_B_mc = rand(dist_B, 5000)

mean(θ_B_mc .< θ_A_mc)

dist_θ_B = n -> Gamma(a₀_B*n + sy_B, 1/(n + n_B) )

# %%
t_mc = []
for n₀ in 1:50
    θ_B_mc = rand(dist_θ_B(n₀), 5000)
    append!(t_mc, mean(θ_B_mc .< θ_A_mc))
end

θ_A_mc = rand(dist_A, 10000)
θ_B_mc = rand(dist_B, 10000)
y_A_mc = rand.(Poisson.(θ_A_mc))
y_B_mc = rand.(Poisson.(θ_B_mc))

mean(y_A_mc .> y_B_mc)

t_mc = []
for n₀ in 1:50
    θ_B_mc = rand(dist_θ_B(n₀), 10000)
    y_B_mc = rand.(Poisson.(θ_B_mc))
    append!(t_mc, mean(θ_B_mc .< θ_A_mc))
end