# Packages
library(klaR)
library(MASS)

# Data
d <- structure(list(y = structure(c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 1L), .Label = c("0", "1"), class = "factor"), x1 = c(2, 2.8, 1.5, 2.1, 5.5, 8, 6.9, 8.5, 2.5, 7.7), x2 = c(1.5, 1.2, 1, 1, 4, 4.8, 4.5, 5.5, 2, 3.5)), .Names = c("y", "x1", "x2"), row.names = c(NA, -10L), class = "data.frame")

# Naive Bayes Model
mN <- NaiveBayes(y ~ x1+x2, data = d)

# Data

# Class 1
m1 <- mean(d[which(d$y==1),]$x1)
m2 <- mean(d[which(d$y==1),]$x2)
mu1_2 <- c(m1,m2)  # Mean
sd1 <- sd(d[which(d$y==1),]$x1)
sd2 <- sd(d[which(d$y==1),]$x2)
Sigma1_2 <- matrix(c(sd1, 0, 0, sd2), 2)  # Covariance matrix
bivn1_2 <- mvrnorm(5000, mu = mu1_2, Sigma = Sigma1_2 )  # from Mass package: Simulate bivariate normal PDF
bivn1_2.kde <- kde2d(bivn1_2[,1], bivn1_2[,2], n = 50)   # from MASS package: Calculate kernel density estimate


# Class 0
m3 <- mean(d[which(d$y==0),]$x1)
m4 <- mean(d[which(d$y==0),]$x2)
mu3_4 <- c(m3,m4)  # Mean
sd3 <- sd(d[which(d$y==0),]$x1)
sd4 <- sd(d[which(d$y==0),]$x2)
Sigma3_4 <- matrix(c(sd3, 0, 0, sd4), 2)  # Covariance matrix
bivn3_4 <- mvrnorm(5000, mu = mu3_4, Sigma = Sigma3_4 )  # from Mass package: Simulate bivariate normal PDF
bivn3_4.kde <- kde2d(bivn3_4[,1], bivn3_4[,2], n = 50)   # from MASS package: Calculate kernel density estimate


# Plot
plot(x= d$x1, y=d$x2, xlim=c(-1,10), ylim=c(-1,10), col=d$y, pch=19, cex=2, ylab="x2", xlab="x1")
contour(bivn1_2.kde, add = TRUE, col="darkgrey")     # from base graphics package
contour(bivn3_4.kde, add = TRUE, col="darkgrey") # from base graphics package
text(labels = "Class 1",x = 8, y=7, col="grey")
text(labels = "Class 0",x = 0, y=4, col="grey")