Generating Random Probability Vectors

probability_simplex.R

# Uniform

a <- runif(10000, 0, 1)
b <- runif(10000, 0, 1)
c <- runif(10000, 0, 1)

df <- cbind(a, b, c)

df <- transform(df, s = a + b + c)

df <- transform(df, a = a / s)
df <- transform(df, b = b / s)
df <- transform(df, c = c / s)

ggplot(df, aes(x = a, y = b)) + geom_point()

# Negative Log Uniform

a <- -log(runif(10000, 0, 1))
b <- -log(runif(10000, 0, 1))
c <- -log(runif(10000, 0, 1))

df <- cbind(a, b, c)

df <- transform(df, s = a + b + c)

df <- transform(df, a = a / s)
df <- transform(df, b = b / s)
df <- transform(df, c = c / s)

ggplot(df, aes(x = a, y = b)) + geom_point()

# Gamma

a <- rgamma(10000, 1, 1)
b <- rgamma(10000, 1, 1)
c <- rgamma(10000, 1, 1)

df <- cbind(a, b, c)

df <- transform(df, s = a + b + c)

df <- transform(df, a = a / s)
df <- transform(df, b = b / s)
df <- transform(df, c = c / s)

ggplot(df, aes(x = a, y = b)) + geom_point()