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Author: ankitbit

Session-1/our_prior.pptx

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+#####################################################################
+################    SESSION  1   ####################################
+#####################################################################
+
+
+######	beta distribution  ########
+
+
+
+par(mfrow=c(3,3))
+
+for (a in c(0.5,1, 10)) {
+	for (b in c(0.5, 1,10)) {
+
+		plot(function(x)dbeta(x, a, b), xlim=c(0,1), ylab="", xlab = "")
+  		  title(paste("Beta","(","a=",a,",","b=",b,")"))
+	}
+}
+
+
+
+
+######################## smoking rate from Barcelona  ###########################
+
+par(mfrow=c(1,1))
+
+a <- 4
+b <- 6
+
+ 
+plot(function(x)dbeta(x, a, b), xlim=c(0,1), ylab="", xlab = "", lwd=2, col="yellow")
+ title(paste("Beta","(","a=",a,",","b=",b,")"))
+
+
+
+
+################# probability to get head when you throw a coin  ################
+
+par(mfrow=c(1,1))
+
+a <- 100
+b <- 100
+
+ 
+plot(function(x)dbeta(x, a, b), xlim=c(0,1), ylab="", xlab = "")
+ title(paste("Prior distribution: Beta","(","a=",a,",","b=",b,")"))
+
+
+
+#######  DATA
+
+N <- 25
+y <- 11
+
+
+####   likelihood function
+
+k <- integrate(function(th)dbinom(y,N,th), lower=0, upper=1)$value
+
+plot(function(th)dbinom(y,N,th)/k, xlim=c(0,1), xlab=expression(theta), main="likelihood function", add=T, lty=2)
+ legend("topright", c("prior","likelihood"), lty=c(1,2))
+ abline(v=y/N, lty=3)
+
+
+
+
+#######################  height of adult catalan people   ####################
+
+
+prior1 <- c(m=190, s=1)
+
+
+
+#####  prior distribution
+
+plot(function(x)dnorm(x,prior1[1], prior1[2]),xlim=c(120,220), ylab="", xlab = expression(mu),main=paste("Normal(",prior1[1],",",prior1[2],")",sep=""))
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