从 bayesAB 包的 bayesTest 函数手动计算后验预期损失

Question

当我在一些模拟数据上使用该函数时

library(bayesAB)

set.seed(255)

# simulate data
A <- rbinom(250, 1, .25)
B <- rbinom(250, 1, .2)

# apply the function for AB group comparison
AB_test <- bayesTest(A, 
                     B, 
                     priors = c('alpha' = 65, 'beta' = 200), 
                     n_samples = 1e5, 
                     distribution = 'bernoulli')
# obtain the output
summary(AB_test)

我得到以下输出

# Quantiles of posteriors for A and B:
#   
# $Probability
# $Probability$A
# 0%       25%       50%       75%      100% 
# 0.1775006 0.2469845 0.2598399 0.2730324 0.3506919 
# 
# $Probability$B
# 0%       25%       50%       75%      100% 
# 0.1510354 0.2146442 0.2268472 0.2394675 0.3182802 
# 
# 
# --------------------------------------------
#   
# P(A > B) by (0)%: 
#   
# $Probability
# [1] 0.89305
# 
# --------------------------------------------
#   
# Credible Interval on (A - B) / B for interval length(s) (0.9) : 
#   
# $Probability
# 5%         95% 
# -0.04278263  0.37454069 
# 
# --------------------------------------------
#   
# Posterior Expected Loss for choosing A over B:
#   
# $Probability
# [1] 0.00587424

我知道如何使用后验数据手动获取前 3 个部分

quantile(AB_test$posteriors$Probability$A, c(0, 0.25, 0.50, 0.75, 1))

# 0%       25%       50%       75%      100% 
# 0.1775006 0.2469845 0.2598399 0.2730324 0.3506919

quantile(AB_test$posteriors$Probability$B, c(0, 0.25, 0.50, 0.75, 1))

# 0%       25%       50%       75%      100% 
# 0.1510354 0.2146442 0.2268472 0.2394675 0.3182802

mean(AB_test$posteriors$Probability$A > AB_test$posteriors$Probability$B)

# [1] 0.89305

quantile(AB_test$posteriors$Probability$A / AB_test$posteriors$Probability$B - 1, c(0.05, 0.95))

# 5%         95% 
# -0.04278263  0.37454069

但我不确定如何计算输出最后一部分中显示的后验预期损失。这可能吗？

Answer 1

您可以通过查看摘要的创建方式来弄清楚这一点，即控制台中的运行 bayesAB:::summary.bayesTest。我自己做这个我发现：

> lapply(
+     AB_test$posteriors, 
+     function(x) do.call(bayesAB:::getPostError, unname(x))
+ )
$Probability
[1] 0.00587424

控制台中的

运行 bayesAB:::getPostError 准确显示了计算的工作原理：

> bayesAB:::getPostError
function (A_samples, B_samples, f = function(a, b) (a - b)/b) 
{
    BoverA <- B_samples > A_samples
    loss <- f(B_samples, A_samples)
    coalesce(mean(BoverA) * mean(loss[BoverA]))
}
<bytecode: 0x0000017fe9329040>
<environment: namespace:bayesAB>

从 bayesAB 包的 bayesTest 函数手动计算后验预期损失

Calculate posterior expected loss manually from bayesTest function of bayesAB package

r

ab-testing