计算机代考 #JAGS script for normally distributed data with both mean and variance unk – cscodehelp代写
#JAGS script for normally distributed data with both mean and variance unknown
require(rjags)
#generate data (the same we have used for the Gibbs sampler example)
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set.seed(123)
n=150; y=rnorm(n,2,3)
#Prior information for the mean and variance.
#Note that in the BUGS language the normal dist. is parameterised in terms of the precision=1/variance
mu0=0; sigma02=100; a=0.1; b=0.1
#writing the model, in essence similar syntax to WinBUGS/OpenBUGS
model_string <- "model{
# Likelihood
for(i in 1:n){
y[i]~dnorm(mu,inv.var)
# Prior for mu
mu~dnorm(mu0,inv.var0)
inv.var0=1/sigma02
# Prior for the inverse variance
inv.var~dgamma(a, b)
# Compute the variance
sigma2=1/inv.var
data=list(y=y,n=n,mu0=mu0,sigma02=sigma02,a=a,b=b)
#list of initial values (if not supplied, the function jags.model will generate initial values)
inits=list(mu=mean(y),inv.var=1/var(y))
#passing the model to jags *format*
model=jags.model(textConnection(model_string),n.chains=3,data=data,inits=inits)
#Burnin of 1000 samples
update(model,1000,progress.bar="none")
# Running the model
res=coda.samples(model,variable.names=c("mu","sigma2"),n.iter=10000, progress.bar="none")
#summary of the results (posterior mean, std deviation, quantiles,ect)
summary(res)
#trace and density plots for each of the parameters monitored (mu and sigma2 in this case)
#autocorrelation function
autocorr.plot(res)
#gelman rubin statistic (only works when number of chains >=2)
gelman.plot(res)
#extracting the chains for mu and sigma 2
#mu for chain 1
res[[1]][,1]
#sigma2 for chain 1
res[[1]][,2]
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