The BUGS language for declaring statistical models was popularized by WinBUGS, OpenBUGS and JAGS. Those generate and run an MCMC for the model, but they donâ€™t allow a programmer to use the model in any other way. NIMBLE provides a new implementation of the BUGS language and creates model objects you can program with.

NIMBLE supports most models written for BUGS or JAGS. It also extends the BUGS language in a bunch of ways that we wonâ€™t go into here. See the User Manual for more details.

Letâ€™s pick a simple model from the classic WinBUGS examples: the dyes example. This is a simple normal hierarchical model. A description can be found here. A copy of the original is on our GitHub repository here. A modified version we will use is set up like this:

`library(nimble, warn.conflicts = FALSE)`

```
## nimble version 0.12.1 is loaded.
## For more information on NIMBLE and a User Manual,
## please visit https://R-nimble.org.
```

```
dyesCode <- nimbleCode({
# Model
for (i in 1:BATCHES) {
for (j in 1:SAMPLES) {
y[i,j] ~ dnorm(mu[i], sd = sigma.within);
}
mu[i] ~ dnorm(theta, sd = sigma.between);
}
# Priors
theta ~ dnorm(0.0, 1.0E-10);
sigma.within ~ dunif(0, 100)
sigma.between ~ dunif(0, 100)
})
```

Compared to the original, this has been modified by using standard deviation parameters instead of precision parameters in two places â€“ to illustrate NIMBLEâ€™s ability to handle different parameterizations â€“ and by removing the posterior predictive nodes.

By the way, any of the standard WinBUGS examples can be loaded automatically in NIMBLE like this:

`classicDyesModel <- readBUGSmodel('dyes', dir = getBUGSexampleDir('dyes'))`

We can create a model from `dyesCode`

like this:

`dyesModel <- nimbleModel(dyesCode, constants = list(BATCHES = 6, SAMPLES = 5))`

`## Defining model`

`## Building model`

```
## Running calculate on model
## [Note] Any error reports that follow may simply reflect missing values in model variables.
```

`## Checking model sizes and dimensions`

```
## [Note] This model is not fully initialized. This is not an error.
## To see which variables are not initialized, use model$initializeInfo().
## For more information on model initialization, see help(modelInitialization).
```

And we can set data values in it like this:

```
data <- matrix(c(1545, 1540, 1595, 1445, 1595, 1520, 1440, 1555, 1550,
1440, 1630, 1455, 1440, 1490, 1605, 1595, 1515, 1450, 1520, 1560,
1510, 1465, 1635, 1480, 1580, 1495, 1560, 1545, 1625, 1445), nrow = 6)
dyesModel$setData(list(y = data))
dyesModel$y
```

```
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1545 1440 1440 1520 1580
## [2,] 1540 1555 1490 1560 1495
## [3,] 1595 1550 1605 1510 1560
## [4,] 1445 1440 1595 1465 1545
## [5,] 1595 1630 1515 1635 1625
## [6,] 1520 1455 1450 1480 1445
```

It is also possible to set data values when calling `nimbleModel`

.

Now the model is an R object, and we can manipulate it as such.

```
dyesModel$theta <- 1500
dyesModel$mu <- rnorm(6, 1500, 50)
dyesModel$sigma.within <- 20
dyesModel$sigma.between <- 20
dyesModel$y[1,]
```

`## [1] 1545 1440 1440 1520 1580`

`dyesModel$theta`

`## [1] 1500`

```
## arbitrary example
dyesModel$calculate(c('theta', 'mu[1:6]', 'y[,2]'))
```

`## [1] -113.4204`

```
## arbitrary example
dyesModel$mu
```

`## [1] 1534.477 1519.673 1487.251 1458.544 1552.233 1565.561`

```
dyesModel$simulate(c('mu[1:3]'))
dyesModel$mu
```

`## [1] 1503.245 1522.113 1517.607 1458.544 1552.233 1565.561`

```
## arbitrary example
dyesModel$getDependencies(c('theta', 'mu[3]'))
```

```
## [1] "theta" "mu[1]" "mu[2]" "mu[3]" "mu[4]" "mu[5]" "mu[6]"
## [8] "y[3, 1]" "y[3, 2]" "y[3, 3]" "y[3, 4]" "y[3, 5]"
```

`library(igraph)`

```
##
## Attaching package: 'igraph'
```

```
## The following object is masked _by_ '.GlobalEnv':
##
## sizes
```

```
## The following objects are masked from 'package:stats':
##
## decompose, spectrum
```

```
## The following object is masked from 'package:base':
##
## union
```

`plot(dyesModel$getGraph())`

With many nodes, the automatically generated graph can be hard to interpret. Note that arrows indicate node dependencies. The `mu`

nodes depend on the centrally plotted `sigma.within`

, `sigma.between`

, and `theta`

nodes, and the `y`

s depend on their corresponding `mu`

s. The purpose of this illustration is to visualize that NIMBLE models are represented as graphical objects that can be used programmatically.

Finally we can compile the model and use the compiled version the same way we used the uncompiled version above:

`compiled_dyesModel <- compileNimble(dyesModel)`

```
## Compiling
## [Note] This may take a minute.
## [Note] Use 'showCompilerOutput = TRUE' to see C++ compilation details.
```

```
compiled_dyesModel$theta <- 1450
compiled_dyesModel$calculate() ## all nodes by default
```

`## [1] -376.4665`

Naturally, the compiled version is much faster.