---
title: "Introduction to jagsUI"
date: "`r Sys.Date()`"
output:
  markdown::html_format
vignette: >
  %\VignetteIndexEntry{Introduction to jagsUI}
  %\VignetteEngine{knitr::knitr}
  \usepackage[utf8]{inputenc}
---


```{r, echo = FALSE, message = FALSE}
require(jagsUI)
knitr::opts_chunk$set(
  comment = "#",
    error = FALSE,
     tidy = FALSE,
    cache = FALSE,
 collapse = TRUE
)
```

# Installing JAGS

In addition to installing the `jagsUI` package, we also need to separately install the free JAGS software, which you can download [here](https://sourceforge.net/projects/mcmc-jags/files/JAGS/4.x/).

Once that's installed, load the `jagsUI` library:

```{r}
library(jagsUI)
```

# Typical `jagsUI` Workflow

1. Organize data into a named `list`
2. Write model file in the BUGS language
3. Specify initial MCMC values (optional)
4. Specify which parameters to save posteriors for
5. Specify MCMC settings
6. Run JAGS
7. Examine output

# 1. Organize data

We'll use the `longley` dataset to conduct a simple linear regression.
The dataset is built into R.

```{r}
data(longley)
head(longley)
```

We will model the number of people employed (`Employed`) as a function of Gross National Product (`GNP`).
Each column of data is saved into a separate element of our data list.
Finally, we add a list element for the number of data points `n`.
In general, elements in the data list must be numeric, and structured as arrays, matrices, or scalars.

```{r}
jags_data <- list(
  gnp = longley$GNP,
  employed = longley$Employed,
  n = nrow(longley)
)
```

# 2. Write BUGS model file

Next we'll describe our model in the BUGS language.
See the [JAGS manual](https://sourceforge.net/projects/mcmc-jags/files/Manuals/4.x/) for detailed information on writing models for JAGS.
Note that data you reference in the BUGS model must exactly match the names of the list we just created.
There are various ways to save the model file, we'll save it as a temporary file.

```{r}
# Create a temporary file
modfile <- tempfile()

#Write model to file
writeLines("
model{

  # Likelihood
  for (i in 1:n){ 
    # Model data
    employed[i] ~ dnorm(mu[i], tau)
    # Calculate linear predictor
    mu[i] <- alpha + beta*gnp[i]
  }
    
  # Priors
  alpha ~ dnorm(0, 0.00001)
  beta ~ dnorm(0, 0.00001)
  sigma ~ dunif(0,1000)
  tau <- pow(sigma,-2)

}
", con=modfile)
```

# 3. Initial values

Initial values can be specified as a list of lists, with one list element per MCMC chain.
Each list element should itself be a named list corresponding to the values we want each parameter initialized at.
We don't necessarily need to explicitly initialize every parameter. 
We can also just set `inits = NULL` to allow JAGS to do the initialization automatically, but this will not work for some complex models.
We can also provide a function which generates a list of initial values, which `jagsUI` will execute for each MCMC chain.
This is what we'll do below.

```{r}
inits <- function(){  
  list(alpha=rnorm(1,0,1),
       beta=rnorm(1,0,1),
       sigma=runif(1,0,3)
  )  
}
```

# 4. Parameters to monitor

Next, we choose which parameters from the model file we want to save posterior distributions for.
We'll save the parameters for the intercept (`alpha`), slope (`beta`), and residual standard deviation (`sigma`).

```{r}
params <- c('alpha','beta','sigma')
```

# 5. MCMC settings

We'll run 3 MCMC chains (`n.chains = 3`).

JAGS will start each chain by running adaptive iterations, which are used to tune and optimize MCMC performance.
We will manually specify the number of adaptive iterations (`n.adapt = 100`).
You can also try `n.adapt = NULL`, which will keep running adaptation iterations until JAGS reports adaptation is sufficient.
In general you do not want to skip adaptation.

Next we need to specify how many regular iterations to run in each chain in total.
We'll set this to 1000 (`n.iter = 1000`).
We'll specify the number of burn-in iterations at 500 (`n.burnin = 500`).
Burn-in iterations are discarded, so here we'll end up with 500 iterations per chain (1000 total - 500 burn-in).
We can also set the thinning rate: with `n.thin = 2` we'll keep only every 2nd iteration.
Thus in total we will have 250 iterations saved per chain ((1000 - 500) / 2).

The optimal MCMC settings will depend on your specific dataset and model.

# 6. Run JAGS

We're finally ready to run JAGS, via the `jags` function.
We provide our data to the `data` argument, initial values function to `inits`, our vector of saved parameters to `parameters.to.save`, and our model file path to `model.file`.
After that we specify the MCMC settings described above.

```{r}
out <- jags(data = jags_data,
            inits = inits,
            parameters.to.save = params,
            model.file = modfile,
            n.chains = 3,
            n.adapt = 100,
            n.iter = 1000,
            n.burnin = 500,
            n.thin = 2)
```

We should see information and progress bars in the console.

If we have a long-running model and a powerful computer, we can tell `jagsUI` to run each chain on a separate core in parallel by setting argument `parallel = TRUE`:

```{r, eval=FALSE}
out <- jags(data = jags_data,
            inits = inits,
            parameters.to.save = params,
            model.file = modfile,
            n.chains = 3,
            n.adapt = 100,
            n.iter = 1000,
            n.burnin = 500,
            n.thin = 2,
            parallel = TRUE)
```

While this is usually faster, we won't be able to see progress bars when JAGS runs in parallel.

# 7. Examine output

Our first step is to look at the output object `out`:

```{r}
out
```

We first get some information about the MCMC run.
Next we see a table of summary statistics for each saved parameter, including the mean, median, and 95% credible intervals.
The `overlap0` column indicates if the 95% credible interval overlaps 0, and the `f` column is the proportion of posterior samples with the same sign as the mean.

The `out` object is a `list` with many components:

```{r}
names(out)
```

We'll describe some of these below.

## Diagnostics

We should pay special attention to the `Rhat` and `n.eff` columns in the output summary, which are MCMC diagnostics.
The `Rhat` (Gelman-Rubin diagnostic) values for each parameter should be close to 1 (typically, < 1.1) if the chains have converged for that parameter.
The `n.eff` value is the effective MCMC sample size and should ideally be close to the number of saved iterations across all chains (here 750, 3 chains * 250 samples per chain).
In this case, both diagnostics look good.

We can also visually assess convergence using the `traceplot` function:

```{r}
traceplot(out)
```

We should see the lines for each chain overlapping and not trending up or down.

## Posteriors

We can quickly visualize the posterior distributions of each parameter using the `densityplot` function:

```{r}
densityplot(out)
```

The traceplots and posteriors can be plotted together using `plot`:

```{r}
plot(out)
```

We can also generate a posterior plot manually.
To do this we'll need to extract the actual posterior samples for a parameter.
These are contained in the `sims.list` element of `out`.

```{r}
post_alpha <- out$sims.list$alpha
hist(post_alpha, xlab="Value", main = "alpha posterior")
```

## Update

If we need more iterations or want to save different parameters, we can use `update`:

```{r}
# Now save mu also
params <- c(params, "mu")
out2 <- update(out, n.iter=300, parameters.to.save = params)
```

The `mu` parameter is now in the output:

```{r}
out2
```

This is a good opportunity to show the `whiskerplot` function, which plots the mean and 95% CI of parameters in the `jagsUI` output:

```{r}
whiskerplot(out2, 'mu')
```