A common problem in the analysis of experimental data is deciding whether two sets of data samples represent the same underlying process (for example, when deciding whether a particular treatment has had an effect). One way to do this is by using a t-test. However, we can get use nested sampling to solve this problem instead.
Firstly, we load the package:
Then, we'll generate some data. We'll set a number of samples:
n.samples <- 500
and set two different means (and a common standard deviation):
sd.1 <- 2 mean.1 <- 0 sd.2 <- 2 mean.2 <- 1
Now we'll generate three sets of samples. Two have the same mean and standard deviation and the third is different:
data.a <- rnorm(n.samples, mean.1, sd.1) data.b <- rnorm(n.samples, mean.1, sd.1) data.c <- rnorm(n.samples, mean.2, sd.2)
Let's look at the data:
par(mfrow=c(1, 3)) hist(data.a, col='blue') hist(data.b, col='green') hist(data.c, col='red')
Now we can use nested sampling. Here, we use a convenience function that will compare the evidence for the two models:
The function works by calculating the evidence for each model and returning the difference. Firstly, we can look at the evidence that the first two sets of samples are from the same distribution:
##  5.313594
By the Jeffrey's scale, this is substantial evidence in favour. Comparing the first and third:
##  -17.56065
We see that the evidence is strongly against the two sets of samples being from the same distribution (the correct result, given that their means differ).