Bayesian Mixture Model Examples

Mixture of univariate Gaussians, bimodal

x = seq(-5, 12, length=100)
y = 0.6*dnorm(x, 0, 1) + 0.4*dnorm(x, 5, 2)
par(mar=c(4,4,1,1)+0.1)
plot(x, y, type="l", ylab="Density", las=1, lwd=2)

Mixture of univariate Gaussians, unimodal skewed

x = seq(-5, 12, length=100)
y = 0.55*dnorm(x, 0, sqrt(2)) + 0.45*dnorm(x, 3, 4)
par(mar=c(4,4,1,1)+0.1)
plot(x, y, type="l", ylab="Density", las=1, lwd=2)

Mixture of univariate Gaussians, unimodal heavy tail

x = seq(-12, 12, length=100)
y = 0.40*dnorm(x, 0, sqrt(2)) + 
    0.40*dnorm(x, 0, sqrt(16)) + 
    0.20*dnorm(x, 0, sqrt(20))
z = dnorm(x, 0, sqrt(0.4*2+0.4*16+0.2*20))
par(mar=c(4,4,1,1)+0.1)
plot(x, y, type="l", ylab="Density", las=1, lwd=2)
lines(x, z, lty=2, lwd=2)
legend(2, 0.16, c("Mixture","Gaussian"), lty=c(1,2), bty="n", 
       cex=0.77, lwd=c(2,2))