Bayes normal

library(rjags)

## Loading required package: coda

## Linked to JAGS 4.2.0

## Loaded modules: basemod,bugs

library(ggmcmc)

## Loading required package: dplyr

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

## Loading required package: tidyr

## Loading required package: ggplot2

mod <-"model {
    for (i in 1:N) {
        y[i] ~ dnorm(mu, tau)
    }
    mu ~ dunif(0, 10)
    tau <- pow(sigma, -2)
    sigma ~ dunif(0, 100)
}"

y=c(1,2,3)
N=length(y)
data<-list(N=N,y=y)
model<-jags.model(textConnection(mod),data=data)

## Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 3
##    Unobserved stochastic nodes: 2
##    Total graph size: 13
## 
## Initializing model

update(model,n.iter=1000)
output=coda.samples(model=model,variable.names=c("mu"),n.iter=100000,thin=10)
update(model,n.iter=1000)
output=coda.samples(model=model,variable.names=c("mu"),n.iter=100000)
plot(output)

summary(output)

## 
## Iterations = 103001:203000
## Thinning interval = 1 
## Number of chains = 1 
## Sample size per chain = 1e+05 
## 
## 1. Empirical mean and standard deviation for each variable,
##    plus standard error of the mean:
## 
##           Mean             SD       Naive SE Time-series SE 
##       2.388345       1.476242       0.004668       0.013698 
## 
## 2. Quantiles for each variable:
## 
##   2.5%    25%    50%    75%  97.5% 
## 0.3265 1.5327 2.1079 2.8290 6.6932