I'm starting my way in the Bayesian world, and I'm trying to build a simple model for estimating the mean and variance of a normal distribution. I assume that:

Code:

```
y=rnorm(100,50,4) # This would be the data
mu0=0 #Prior of mean
var0=100 #Prior for the variance
#I continue by using the equations from Gelman to do conjugate analysis. (I assume that the #'sample size' on which the prior is based on is 1).
mu1=(n0*mu0+length(y)*mean(y))/(n0+nx) #posterior mean
var1=(n0*var0+var(y)*length(y)+(n0*nx/(n0+nx))*(mu0-mean(y))^2)/(n0+nx) #posterior variance
meanUncertainty=var1/(n0+nx) #Variance of the posterior distribution of the mean
#I could also build distributions for var1 and mu1 as follows:
postVarDist=rinvgamma(10000,shape=(dataN+priorN)/2,rate=(postVar*(dataN+priorN))/2)
postMeanDist=rt(10000,priorN)*meanUncertainty+postMean # A scale-shifting t distribution
```

Now I build a JAGS model as follows:

Code:

```
#The datalist:
datalist=list(priorMean=0,
y=y,
var0=1000,
meanUncertainty=1000/1,
n0=1,
nx=length(data))
#The model
for (i in 1:dataN){
y[i]~dnorm(mu1,tau)
}
tau~dgamma(n0/2,(n0*var0)/2)
postMean~dnorm(mu0,1/meanUncertainty)
postVar<-1/tau
```

I'm really trying to figure out what I did wrong in any of the models. I noticed that if in the analytical solution I define var1=(n0*var0+var(y)*length(y) (Thus ignoring the 'prediction error' - the distance between mean(y) and mu0), I get similar results. What does it means? Is the distribution I get in JAGS for the variance a marginal or a P(var/mu) distribution?

Any help would be very much appreciated.

Isaac Fradkin