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# Bayesian model selection and statistical modeling 
# Chapman & Hall/CRC Taylor and Francis Group 
#
# Chapter2: Section2.8.2
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# Smoothing parameter selection
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# Author : Tomohiro Ando
#
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# Data generation

n <- 50

x <- sort(runif(n,-1,1))
z <- 0.3*cos(pi*x)+0.5*sin(2*pi*x)
y <- z+rnorm(n,0,0.2)

# Design matrix

X <- cbind(x^1,x^2,x^3,x^4,x^5,x^6,x^7,x^8,x^9,x^10,x^11,x^12,x^13,x^14,x^15)

# Models

A <- 10^-6*diag(1,ncol(X)) #Model 1
#A <- 10^-3*diag(1,ncol(X)) #Model 2
#A <- 10^-1*diag(1,ncol(X)) #Model 3
#A <- 10^1*diag(1,ncol(X)) #Model 4

# Plot 

library(akima)
B    <- solve(t(X)%*%X+A)%*%t(X)%*%y
yhat <- X%*%matrix(B,ncol=1)
plot(x,y)
lines(x,yhat,lty=2)
lines(x,z,lty=1)