Forked from rmcelreath/prior_likelihood_conflict.r
Created
September 12, 2023 10:09
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Demonstration of how normal and student-t distributions interact in Bayesian updating
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# prior - likelihood conflict | |
library(rethinking) | |
yobs <- 0 | |
mtt <- ulam( | |
alist( | |
y ~ dstudent(2,mu,1), | |
mu ~ dstudent(2,10,1) | |
), data=list(y=yobs) , chains=4 , iter=2000 ) | |
mnn <- ulam( | |
alist( | |
y ~ dnorm(mu,1), | |
mu ~ dnorm(10,1) | |
), data=list(y=yobs) , chains=4 , iter=2000) | |
mtn <- ulam( | |
alist( | |
y ~ dstudent(2,mu,1), | |
mu ~ dnorm(10,1) | |
), data=list(y=yobs) , chains=4 , iter=2000) | |
mnt <- ulam( | |
alist( | |
y ~ dnorm(mu,1), | |
mu ~ dstudent(2,10,1) | |
), data=list(y=yobs) , chains=4 , iter=2000) | |
# plot | |
par(mfrow=c(2,2),cex=1.05) | |
ymax <- 0.53 | |
xlwd <- 1.5 | |
postcol <- 2 | |
xadj <- 0.8 | |
p <- extract.samples(mnn) | |
dens(p$mu, xlim=c(-5,15), ylim=c(0,ymax), lwd=xlwd+1 , col=postcol, xlab="" ,adj=xadj ) | |
#mtext("normal prior, normal likelihood") | |
curve( dnorm(yobs,x,1) , add=TRUE , lty=1 , lwd=xlwd ) # lik | |
curve( dnorm(x,10,1) , add=TRUE , lty=2 , lwd=xlwd ) # prior | |
text(0,0.42,"likelihood") | |
text(10,0.42,"prior") | |
p <- extract.samples(mtt) | |
dens(p$mu , xlim=c(-5,15) , ylim=c(0,ymax) , lwd=xlwd+1 , col=postcol , xlab="" ,adj=xadj ) | |
#mtext("t prior, t likelihood") | |
curve( dstudent(yobs,2,x,1) , add=TRUE , lty=1 , lwd=xlwd ) # lik | |
curve( dstudent(x,2,10,1) , add=TRUE , lty=2 , lwd=xlwd ) # prior | |
text(0,0.42,"likelihood") | |
text(10,0.42,"prior") | |
p <- extract.samples(mnt) | |
dens(p$mu, xlim=c(-5,15), ylim=c(0,ymax), lwd=xlwd+1 , col=postcol, xlab="" ,adj=xadj ) | |
#mtext("t prior, normal likelihood") | |
curve( dnorm(yobs,x,1) , add=TRUE , lty=1 , lwd=xlwd) # lik | |
curve( dstudent(x,2,10,1) , add=TRUE , lty=2 , lwd=xlwd) # prior | |
text(0,0.42,"likelihood") | |
text(10,0.42,"prior") | |
p <- extract.samples(mtn) | |
dens(p$mu, xlim=c(-5,15), ylim=c(0,ymax), lwd=xlwd+1 , col=postcol, xlab="" ,adj=xadj ) | |
#mtext("normal prior, t likelihood") | |
curve( dstudent(yobs,2,x,1) , add=TRUE , lty=1 , lwd=xlwd) # lik | |
curve( dnorm(x,10,1) , add=TRUE , lty=2 , lwd=xlwd) # prior | |
text(0,0.42,"likelihood") | |
text(10,0.42,"prior") |
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