##In this example:
n=50; xbar=0.62; xgbar=0.46; s=0.4
#prior beliefs: 
a=2;b=1
c=3;d=1

library(nclbayes)
posterior = mwgGamma(N=20000, initial=(a/b), innov=0.9, priorparam=c(2,1,3,1), n=50, xbar=0.62, xgbar=0.46, show=TRUE)
mcmcAnalysis(posterior, rows=2, show=FALSE)
plot(posterior, type="l")

#What if we had a bad starting value for alpha?
posterior = mwgGamma(N=20000, initial=50, innov=0.9, priorparam=c(2,1,3,1), n=50, xbar=0.62, xgbar=0.46, show=TRUE)
mcmcAnalysis(posterior, rows=2, show=FALSE)
plot(posterior, type="l")

#What if the innovation variance was too high? Chain too "hot" (Acceptance rates too low)
posterior = mwgGamma(N=20000, initial=(a/b), innov=90, priorparam=c(2,1,3,1), n=50, xbar=0.62, xgbar=0.46, show=TRUE)
mcmcAnalysis(posterior, rows=2, show=FALSE)
plot(posterior, type="l")

#What if the innovation variance was too low? Chain too "cold" (Acceptance rates too high)
posterior = mwgGamma(N=20000, initial=(a/b), innov=0.009, priorparam=c(2,1,3,1), n=50, xbar=0.62, xgbar=0.46, show=TRUE)
mcmcAnalysis(posterior, rows=2, show=FALSE)
plot(posterior, type="l")

#Go back to the Goldilocks example, with bad starting value:
posterior = mwgGamma(N=20000, initial=20, innov=0.9, priorparam=c(2,1,3,1), n=50, xbar=0.62, xgbar=0.46, show=TRUE)
mcmcAnalysis(posterior, rows=2, show=FALSE)
plot(posterior, type="l")

#Burn-in of 50?  Say 500 to be sure!  And thin by 20??
posterior2 = mcmcProcess(input = posterior, burnin=500, thin=20)
mcmcAnalysis(posterior2, rows=2)
mcmcCi(posterior2)