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Simulated sensor network- RAM.R
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#Generating simulated points
set.seed(6)
X<- matrix(round(runif(18),2),ncol = 2)
X
par(mfrow=c(1,1))
plot(X[,1],X[,2],pch=as.character(1:9),col=c(rep(1,6),rep(2,3)), xlim = c(0.15, 1.1),
ylim = c(-0.2, 1.1),xlab="x-coordinate",ylab="y-coordinate",main='Sensor network- 9 nodes')
dist(X)
distance<- matrix(0,nrow = 9,ncol = 9)
distance
norm2 <- function(loca, locb) {
sqrt(sum((loca - locb)^2))
}
for (i in 1:9){
for (j in 1:9){
distance[i,j]=norm2(X[i,],X[j,])
}
}
#Add random error
obs_distance = distance + matrix(rnorm(81,0,0.02),nrow = 9)
for (i in 1:9){
obs_distance[i:9,i]=0
}
obs_distance
#Now we randomly remove some distance by randomly selecting 0 and 1
set.seed(1)
O <- matrix(rbinom(81,1,0.5),nrow=9)
O
for (i in 1:9){
O[i:9,i]=0
}
O
O <- O + t(O)
O
obs_distance
Y = O*obs_distance
Y <- Y + t(Y)
Y
##Distance (binary) of 7th,8th and 9th to 1-6th
Ob<-O[1:6,7:9]
Ob
Os<-O[1:6,1:6]
Os
#The true locations of 7th-9th sensor
Xb <- X[7:9,]
Xb
#The location of unknown sensors (1-6)
Xs <- X[1:6,]
Xs
#Distance of 7,8,9 to 1st 6 points and within 1st 6 points
Yb <- Y[1:6,7:9]
Yb
Ys <- Y[1:6,1:6]
Ys
######## Target joint posterior density
l.target <- function(loc, R = 0.3, sigma = 0.02, Ob, Os, Xb, Xs, Yb, Ys) {
First.term <- NULL
for (i in 1 : 3) {
TEMP <- sapply(1 : 6, function(j) {
exp(-norm2(Xb[i, ], loc[(2 * j -1) : (2 * j)])^2 / 2 / R^2 * Ob[j, i]) *
(1 - exp(-norm2(Xb[i, ], loc[(2 * j -1) : (2 * j)])^2 / 2 / R^2))^(1 - Ob[j, i])
})
First.term <- c(First.term, TEMP)
}
Second.term <- NULL
for (i in 1 : 5) {
TEMP <- sapply((i + 1) : 6, function(j) {
exp(-norm2(loc[(2 * i -1) : (2 * i)],
loc[(2 * j -1) : (2 * j)])^2 / 2 / R^2 * Os[i, j]) *
(1 - exp(-norm2(loc[(2 * i -1) : (2 * i)],
loc[(2 * j -1) : (2 * j)])^2 / 2 / R^2))^(1 - Os[i, j])
})
Second.term <- c(Second.term, TEMP)
}
First.obs.term <- NULL
for (i in 1 : 3) {
TEMP <- sapply(1 : 6, function(j) {
dnorm(Yb[j, i], mean = norm2(Xb[i, ], loc[(2 * j -1) : (2 * j)]),
sd = sigma)^Ob[j, i]
})
First.obs.term <- c(First.obs.term, TEMP)
}
Second.obs.term <- NULL
for (i in 1 : 5) {
TEMP <- sapply((i + 1) : 6, function(j) {
dnorm(Ys[i, j], mean = norm2(loc[(2 * i -1) : (2 * i)],
loc[(2 * j -1) : (2 * j)]),
sd = sigma)^Os[i, j]
})
Second.obs.term <- c(Second.obs.term, TEMP)
}
log.lik <- sum(log(c(First.term, Second.term, First.obs.term, Second.obs.term)))
post <- log.lik + sum(dnorm(loc, mean = rep(0, 12), sd = rep(10, 12), log = TRUE))
post
}
######## RAM
ram.kernel <- function(current.location, current.aux, loc.number, scale) {
eps <- 10^(-308)
accept <- 0
x.c <- current.location
log.x.c.den <- l.target(x.c, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
x.c.den <- exp(log.x.c.den)
z.c <- current.aux
log.z.c.den <- l.target(z.c, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
z.c.den <- exp(log.z.c.den)
# downhill
x.p1 <- x.c
x.p1[(2 * loc.number - 1) : (2 * loc.number)] <- x.p1[(2 * loc.number - 1) : (2 * loc.number)] +
rnorm(2, 0, scale)
log.x.p1.den <- l.target(x.p1, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
x.p1.den <- exp(log.x.p1.den)
N.d <- 1
while (-rexp(1) > log(x.c.den + eps) - log(x.p1.den + eps)) {
x.p1 <- x.c
x.p1[(2 * loc.number - 1) : (2 * loc.number)] <- x.p1[(2 * loc.number - 1) : (2 * loc.number)] +
rnorm(2, 0, scale)
log.x.p1.den <- l.target(x.p1, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
x.p1.den <- exp(log.x.p1.den)
N.d <- N.d + 1
}
# uphill
x.p2 <- x.p1
x.p2[(2 * loc.number - 1) : (2 * loc.number)] <- x.p2[(2 * loc.number - 1) : (2 * loc.number)] +
rnorm(2, 0, scale)
log.x.p2.den <- l.target(x.p2, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
x.p2.den <- exp(log.x.p2.den)
N.u <- 1
while (-rexp(1) > log(x.p2.den + eps) - log(x.p1.den + eps)) {
x.p2 <- x.p1
x.p2[(2 * loc.number - 1) : (2 * loc.number)] <- x.p2[(2 * loc.number - 1) : (2 * loc.number)] +
rnorm(2, 0, scale)
log.x.p2.den <- l.target(x.p2, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
x.p2.den <- exp(log.x.p2.den)
N.u <- N.u + 1
}
# downhill for N.d
N.dz <- 1 # number of total downhill trials for estimate
z <- x.p2
z[(2 * loc.number - 1) : (2 * loc.number)] <- z[(2 * loc.number - 1) : (2 * loc.number)] +
rnorm(2, 0, scale)
log.z.den <- l.target(z, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
z.den <- exp(log.z.den)
while (-rexp(1) > log(x.p2.den + eps) - log(z.den + eps)) {
z <- x.p2
z[(2 * loc.number - 1) : (2 * loc.number)] <- z[(2 * loc.number - 1) : (2 * loc.number)] +
rnorm(2, 0, scale)
log.z.den <- l.target(z, 0.3, 0.02, Ob, Os, Xb, Xs, Yb, Ys)
z.den <- exp(log.z.den)
N.dz <- N.dz + 1
}
# accept or reject the proposal
min.nu <- min(1, (x.c.den + eps) / (z.c.den + eps))
min.de <- min(1, (x.p2.den + eps) / (z.den + eps))
l.mh <- log.x.p2.den - log.x.c.den + log(min.nu) - log(min.de)
if (l.mh > -rexp(1)) {
x.c <- x.p2
z.c <- z
accept <- 1
}
c(x.c, z.c, N.d, N.u, N.dz, accept)
}
MHwG.RAM <- function(initial.loc, initial.aux, jump.scale,
Ob, Os, Xb, Xs, Yb, Ys, n.sample = 10, n.burn = 10) {
print(Sys.time())
n.total <- n.sample + n.burn
accept <- matrix(0, nrow = n.total, ncol = 6)
out <- matrix(NA, nrow = n.total, ncol = 12)
loc.t <- initial.loc
aux.t <- initial.aux
Nd <- matrix(NA, nrow = n.total, ncol = 6)
Nu <- matrix(NA, nrow = n.total, ncol = 6)
Nz <- matrix(NA, nrow = n.total, ncol = 6)
for (i in 1 : n.total) {
for (j in 1 : 6) {
TEMP <- ram.kernel(loc.t, aux.t, j, jump.scale[j])
loc.t <- TEMP[1 : 12]
aux.t <- TEMP[13 : 24]
Nd[i, j] <- TEMP[25]
Nu[i, j] <- TEMP[26]
Nz[i, j] <- TEMP[27]
accept[i, j] <- TEMP[28]
}
out[i, ] <- loc.t
}
print(Sys.time())
list(x = out[-c(1 : n.burn), ],
accept = accept[-c(1 : n.burn), ],
N.d = Nd[-c(1 : n.burn), ],
N.u = Nu[-c(1 : n.burn), ],
N.z = Nz[-c(1 : n.burn), ])
}
j.scale <- rep(1.08, 6) #SD for proposal density
#We run RAM for 250000 iterations with burin-in of 50000
res.ram <- MHwG.RAM(runif(12), runif(12), jump.scale = j.scale,
Ob, Os, Xb, Xs, Yb, Ys,
n.sample = 250000, n.burn = 50000)
res.ram_9sensor <- res.ram$x
########Trace plots
par(mfrow=c(2,3))
plot(1:250000,res.ram_9sensor[,1],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[11])))
plot(1:250000,res.ram_9sensor[,2],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[12])))
plot(1:250000,res.ram_9sensor[,3],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[21])))
plot(1:250000,res.ram_9sensor[,4],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[22])))
plot(1:250000,res.ram_9sensor[,5],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[31])))
plot(1:250000,res.ram_9sensor[,6],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[32])))
mtext("Trace Plot", outer = TRUE, cex = 1.5, line=-2)
par(mfrow=c(2,3))
plot(1:250000,res.ram_9sensor[,7],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[41])))
plot(1:250000,res.ram_9sensor[,8],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[42])))
plot(1:250000,res.ram_9sensor[,9],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[51])))
plot(1:250000,res.ram_9sensor[,10],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[52])))
plot(1:250000,res.ram_9sensor[,11],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[61])))
plot(1:250000,res.ram_9sensor[,12],type='l',xlab = 'Iterations',ylab='Density',main = expression(paste(X[62])))
mtext("Trace Plot", outer = TRUE, cex = 1.5, line=-2)
# Scatterplots
par(mfrow = c(2,3))
plot(res.ram_9sensor[, c(1, 2)], pch = 46, xlab = "", ylab = "", main = "")
title(expression(bold(paste("RAM: ", x[1]))))
mtext(side = 1, text = expression(bold(x[11])), line = 1.6, cex = 1.2)
mtext(side = 2, text = expression(bold(x[12])), line = 1.9, cex = 1.2)
abline(v = Xs[1,1], lty = 2, lwd = 1)
abline(h = Xs[1,2], lty = 2, lwd = 1)
plot(res.ram_9sensor[, c(3, 4)], pch = 46, xlab = "", ylab = "", main = "")
title(expression(bold(paste("RAM: ", x[2]))))
mtext(side = 1, text = expression(bold(x[21])), line = 1.6, cex = 1.2)
mtext(side = 2, text = expression(bold(x[22])), line = 1.9, cex = 1.2)
abline(v = Xs[2,1], lty = 2, lwd = 1)
abline(h = Xs[2,2], lty = 2, lwd = 1)
plot(res.ram_9sensor[, c(5, 6)], pch = 46, xlab = "", ylab = "", main = "")
title(expression(bold(paste("RAM: ", x[3]))))
mtext(side = 1, text = expression(bold(x[31])), line = 1.6, cex = 1.2)
mtext(side = 2, text = expression(bold(x[32])), line = 1.9, cex = 1.2)
abline(v = Xs[3,1], lty = 2, lwd = 1)
abline(h = Xs[3,2], lty = 2, lwd = 1)
plot(res.ram_9sensor[, c(7, 8)], pch = 46, xlab = "", ylab = "", main = "")
title(expression(bold(paste("RAM: ", x[4]))))
mtext(side = 1, text = expression(bold(x[41])), line = 1.6, cex = 1.2)
mtext(side = 2, text = expression(bold(x[42])), line = 1.9, cex = 1.2)
abline(v = Xs[4,1], lty = 2, lwd = 1)
abline(h = Xs[4,2], lty = 2, lwd = 1)
plot(res.ram_9sensor[, c(9, 10)], pch = 46, xlab = "", ylab = "", main = "")
title(expression(bold(paste("RAM: ", x[5]))))
mtext(side = 1, text = expression(bold(x[51])), line = 1.6, cex = 1.2)
mtext(side = 2, text = expression(bold(x[52])), line = 1.9, cex = 1.2)
abline(v = Xs[5,1], lty = 2, lwd = 1)
abline(h = Xs[5,2], lty = 2, lwd = 1)
plot(res.ram_9sensor[, c(11, 12)], pch = 46, xlab = "", ylab = "", main = "")
title(expression(bold(paste("RAM: ", x[6]))))
mtext(side = 1, text = expression(bold(x[61])), line = 1.6, cex = 1.2)
mtext(side = 2, text = expression(bold(x[62])), line = 1.9, cex = 1.2)
abline(v = Xs[6,1], lty = 2, lwd = 1)
abline(h = Xs[6,2], lty = 2, lwd = 1)
#Histogram & Density plots
par(mfrow = c(3,4))
hist(res.ram_9sensor[, 1],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[11])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[11]))))
lines(density(res.ram_9sensor[, 1]), lwd = 1.5)
abline(v = Xs[1,1], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 2],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[12])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[12]))))
lines(density(res.ram_9sensor[, 2]), lwd = 1.5)
abline(v = Xs[1,2], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 3],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[21])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[21]))))
lines(density(res.ram_9sensor[, 3]), lwd = 1.5)
abline(v = Xs[2,1], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 4],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[22])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[22]))))
lines(density(res.ram_9sensor[, 4]), lwd = 1.5)
abline(v = Xs[2,2], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 5],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[31])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[31]))))
lines(density(res.ram_9sensor[, 5]), lwd = 1.5)
abline(v = Xs[3,1], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 6],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[32])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[32]))))
lines(density(res.ram_9sensor[, 6]), lwd = 1.5)
abline(v = Xs[3,2], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 7],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[41])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[41]))))
lines(density(res.ram_9sensor[, 7]), lwd = 1.5)
abline(v = Xs[4,1], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 8],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[42])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[42]))))
lines(density(res.ram_9sensor[, 8]), lwd = 1.5)
abline(v = Xs[4,2], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 9],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[51])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[51]))))
lines(density(res.ram_9sensor[, 9]), lwd = 1.5)
abline(v = Xs[5,1], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 10],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[52])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[52]))))
lines(density(res.ram_9sensor[, 10]), lwd = 1.5)
abline(v = Xs[5,2], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 11],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[61])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[61]))))
lines(density(res.ram_9sensor[, 11]), lwd = 1.5)
abline(v = Xs[6,1], lty = 2, lwd = 2)
hist(res.ram_9sensor[, 12],30,freq = FALSE, main = "", xlab = "", ylab = "")
mtext(side = 1, text = expression(bold(x[62])), line = 1.6, cex = 1.2)
mtext(side = 2, text = "Density", line = 1.7, cex = 1.2, las = 0)
title(expression(bold(paste("RAM: ", x[62]))))
lines(density(res.ram_9sensor[, 12]), lwd = 1.5)
abline(v = Xs[6,2], lty = 2, lwd = 2)