# 
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

sigma_n = 1
sigma_s = 2 # we assume that sigma_s > sigma_n 
p = 0.25
alpha = 0.75

l1_grid = seq( -10, +10, length.out=100 )
l2_grid = seq( -10, +10, length.out=100 )

A = sigma_n / sqrt( sigma_n^2 + sigma_s^2 ) # leading coefficient
C = sigma_s^2 / ( 2 * sigma_n^2 * ( sigma_n^2 + sigma_s^2 ) ) # factor in the exponential

Lambda_1 = A * exp( C * l1_grid )
Lambda_2 = A * exp( C * l2_grid )

#postscript("../../WriteUp/Graphics/Chapter2/prob_2.3.5.eps", onefile=FALSE, horizontal=FALSE)

# First decision region :
#
Pt_1 = Lambda_1 - (1/p) + 2
Pt_2 = - ( alpha - 1 ) * Lambda_2
D1 = outer( Pt_1, Pt_2, FUN="+" )
contour( l1_grid, l2_grid, D1, levels=c(0), xlab="l_1", ylab="l_2", col="black" )

# Second decision region ( a duplicate of the first ):
#
Pt_1 = Lambda_2 - (1/p) + 2
Pt_2 = - ( alpha - 1 ) * Lambda_1
D2 = outer( Pt_1, Pt_2, FUN="+" )
contour( l1_grid, l2_grid, D2, levels=c(0), add=T, xlab="l_1", ylab="l_2", col="red" )

# Third decision region :
#
Pt_1 = Lambda_2
Pt_2 = - Lambda_1
D3 = outer( Pt_1, Pt_2, FUN="+" )
contour( l1_grid, l2_grid, D3, levels=c(0), add=T, xlab="l_1", ylab="l_2", col="green" )

text( 6, -2.5, "H_1" )
text( 0, -2.5, "H_0" )
text( -2.5, 0, "H_0" )
text( 0, 9, "H_2" )

#dev.off()