---
title: "Stat. 481 Pumps Example"
output: html_notebook
---

```{r}
require(rjags) 

source("DBDA2E-utilities.R") 
```
JAGS need the data to be in a list of values, vectors, and matrices.

```{r}
dataList <- list(t = c(94.3, 15.7, 62.9, 126, 5.24, 31.4, 1.05, 1.05, 2.1, 10.5),
   x = c( 5, 1, 5, 14, 3, 19, 1, 1, 4, 22), N = 10)

dataList
```

# Model

```{r}
modelString <- "
   model
   {
      for (i in 1 : N) {
         theta[i] ~ dgamma(alpha, beta)
         lambda[i] <- theta[i] * t[i]
         x[i] ~ dpois(lambda[i])
      }
      alpha ~ dexp(1)
      beta ~ dgamma(0.1, 1.0)
   }
"
```

# Inits

```{r}
initsList <- list(alpha = 1, beta = 1)
```

# Updates

```{r}
jagsModel <- jags.model( file = textConnection(modelString), 
                         data = dataList, 
                         inits = initsList, 
                         n.chains = 5, 
                         n.adapt = 10000 )

update( jagsModel , n.iter=5000 )  # Burn-in

codaSamples = coda.samples( jagsModel,
                            variable.names=c("alpha","beta","theta","lambda"),
                            n.iter=5000 )     # Record sampled values

save( codaSamples , file=paste0("Mcmc.Rdata") )
```

# Examine the chains:
# Convergence diagnostics:

```{r}
plot(codaSamples)
```

```{r}
diagMCMC( codaObject=codaSamples, parName="alpha" )
diagMCMC( codaObject=codaSamples, parName="beta" )
```

```{r}
traceplot(codaSamples)
```

```{r}
plotPost( codaSamples[,"alpha"], main="alpha", xlab=bquote(alpha) )
plotPost( codaSamples[,"beta"], main="beta", xlab=bquote(beta) )
```

```{r}
summary(codaSamples)
```