Complete MaP estimation

ch08.r

@@ -98,3 +98,38 @@ title("Truncated Poisson")
 lines(theta, L, lwd=6, col="#0000BF")
 grid()
 
+#############
+# Chapter 8.3 Maximum-a-Posteriori Estimation
+
+## Influence of the priors
+
+# R code
+N = 5
+mu0 = 0.0
+sigma0 = 1
+theta = 5
+x = rnorm(N, 5, 1)
+xbar = mean(x)
+t = seq(-3, 7, (10)/1000)
+
+q = numeric(1000)
+for (i in 1:N) {
+    x = abs(t-x[i])
+    a = min(x)
+    q[match(a, x)] = 0.1 
+}
+
+thetahat = (sigma0^2. * xbar + mu0/N)/(sigma0^2. + 1. /N)
+sigmahat = sqrt(1. / (1. / sigma0^2 + N))
+p0 = dnorm(t, xbar, 1.)
+p1 = dnorm(t, thetahat, sigmahat)
+prior = dnorm(t, mu0, sigma0)/10
+plot(t, p1, type="n")
+title("N = 5")
+legend(-2, 0.9, legend=c("Likelihood", "Posterior", "Prior", "Data"), col=c("blue", "orange", "green", "purple"), lty=1:1)
+lines(t, p0, lwd = 4, col="blue")
+lines(t, p1, lwd = 4, col="orange")
+lines(t, prior, lwd = 4, col="green")
+lines(t, q, lwd = 4, col="purple")
+grid()
+