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library(ggplot2)
scaleFactor <- 4
scaleFactor2 <- 3
scalePower <- 0.2
firstMean <- 0
secondMeans <- seq(0.05, 0.8, 0.05)
constVar <- 0.12
xlims <- c(-2,2)
pdf('llr_test.pdf', width=10)
for (secondMean in secondMeans){
secondMean <- firstMean + secondMean
test_vals <- seq(xlims[1], xlims[2], 0.05)
ref_diffs <- test_vals - firstMean
alt_diffs <- test_vals - secondMean
scale_diffs <- test_vals - ((firstMean + secondMean) / 2)
space_btwn <- (firstMean - secondMean)^2
dat <- rbind.data.frame(
data.frame(value=log(dnorm(test_vals, firstMean) / dnorm(test_vals, secondMean)), x=test_vals,
type='Log Likelihood Ratio'),
data.frame(value=exp(-(scale_diffs^2) / (scaleFactor * constVar)) * ((alt_diffs)^2 - (ref_diffs)^2) /
(constVar * space_btwn^scalePower * scaleFactor2), x=test_vals,
type='Outlier-Robust LLR'),
data.frame(value=dnorm(test_vals, firstMean, sqrt(constVar)), x=test_vals, type='Canonical Expected\nSignal Level'),
data.frame(value=dnorm(test_vals, secondMean, sqrt(constVar)), x=test_vals, type='Alternative Expected\nSignal Level')
)
print(ggplot(dat) + geom_density(aes(x=x, y=value, fill=type), stat='identity', color='white', size=0, alpha=0.3) +
theme_bw() + ggtitle(paste('Expected Signal Level Difference:', secondMean)) + ylim(-2,2) + xlim(xlims[1],xlims[2]))
}
foo <- dev.off()
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