```
library(ncdDetectTools)
context("ncdDetectOverdispersion")
test_that("Betabinomial (overdispersion) distribution 2 columns",{
predictions <- matrix(c(0.999, 0.001), 1000, 2, byrow = T)
scores <- matrix(c(0,1), 1000, 2, byrow = T)
observed_score <- 10
overdispersion <- 0.3
res <- ncdDetectOverdispersion(predictions, scores, overdispersion, N = 100, method = "naive", observed_score = observed_score)
score_dist <- rbindlist(res$score_dist_overdispersion)[, .("probability" = sum(probability*weight)), by = y]
res_naive_10 <- score_dist[y >= 10, sum(probability)]
bbinom_p_value <- VGAM::dbetabinom(10, 1000, 0.001, overdispersion^2*0.001/(1-0.001), log = T)
expect_lt(abs(log(res_naive_10)-bbinom_p_value), log(3)) # Within a factor 2 using the naive approach
})
test_that("Betabinomial (overdispersion) distribution 3 columns",{
predictions <- matrix(c(0.999, 0.0005, 0.0005), 1000, 3, byrow = T)
scores <- matrix(c(0,1,1), 1000, 3, byrow = T)
observed_score <- c(5, 10)
overdispersion <- 0.3
# Naive method with N = 10,000
# score p_value type
# 1: 5 7.346926e-03 naive
# 2: 10 2.702902e-06 naive
# 3: 5 3.636878e-03 no_overdispersion
# 4: 10 1.074283e-07 no_overdispersion
# Numeric Integration
res_numer <- ncdDetectOverdispersion(predictions, scores, overdispersion, N = 100, method = "numeric", observed_score = observed_score)
score_dist <- rbindlist(res_numer$score_dist_overdispersion)[, .("probability" = sum(probability*weight)), by = y]
score_dist_no_od <- res_numer$score_dist_no_overdispersion
# Expect overdispersion correction gives less significant p-values
res_numer_5 <- score_dist[y >= 5, sum(probability)]
res_numer_10 <- score_dist[y >= 10, sum(probability)]
expect_gt( res_numer_5, score_dist_no_od[y >= 5, sum(probability)])
expect_gt( res_numer_10, score_dist_no_od[y >= 10, sum(probability)] )
# Expect reasonably close to value obtained by naive sampling
expect_lt( abs(log(res_numer_5) - log(7.346926e-03)), log(1.50)) # With-in 50% of the correct value
expect_lt( abs(log(res_numer_10) - log(2.702902e-06)), log(1.50))
})
```

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