NIMBLE is a hierarchical modeling package that uses nearly the same
modeling language as the popular MCMC packages WinBUGS, OpenBUGS and
JAGS. NIMBLE makes the modeling language extensible — you can add
distributions and functions — and also allows customization of MCMC or
other algorithms that use models. Here is a quick summary of steps to
convert existing code from WinBUGS, OpenBUGS or JAGS to NIMBLE. For more
information, see the NIMBLE User
Manual.

# Main steps for converting existing code

These steps assume you are familiar with running WinBUGS, OpenBUGS or
JAGS through an R package such as R2WinBUGS, R2jags, rjags, or
jagsUI.

Wrap your model code in `nimbleCode({})`

, directly in
R.

This replaces the step of writing or generating a separate file
containing the model code.

Alternatively, you can read standard JAGS- and BUGS-formatted
code and data files using `readBUGSmodel`

.

Provide information about missing or empty indices.

- Example: If
`x`

is a matrix, you must write at least
`x[,]`

to show it has two dimensions.
- If other declarations make the size of
`x`

clear,
`x[,]`

will work in some circumstances.
- If not, either provide index ranges (e.g.
`x[1:n, 1:m]`

)
or use the `dimensions`

argument to `nimbleModel`

to provide the sizes in each dimension.

Choose how you want to run MCMC.

Use `nimbleMCMC()`

as the just-do-it way to run an
MCMC. This will take all steps to set up and run an MCMC using NIMBLE’s
default configuration.

To use NIMBLE’s full flexibility: build the model, configure and
build the MCMC, and compile both the model and MCMC. Then run the MCMC
via `runMCMC`

or by calling the `run`

function of
the compiled MCMC. See the NIMBLE User Manual to learn more about what
you can do.

See below for a list of some more nitty-gritty additional steps you
may need to consider for some models.

# Example: An animal abundance model

This example is adapted from Chapter 6, Section 6.4 of *Applied
Hierarchical Modeling in Ecology: Analysis of distribution, abundance
and species richness in R and BUGS. Volume I: Prelude and Static
Models* by Marc Kéry and J. Andrew Royle (2015, Academic Press).
The book’s
web site provides code for its examples.

## Original code

The original model code looks like this:

```
cat(file = "model2.txt", "
model {
# Priors
for(k in 1:3){ # Loop over 3 levels of hab or time factors
alpha0[k] ~ dunif(-10, 10) # Detection intercepts
alpha1[k] ~ dunif(-10, 10) # Detection slopes
beta0[k] ~ dunif(-10, 10) # Abundance intercepts
beta1[k] ~ dunif(-10, 10) # Abundance slopes
}
# Likelihood
# Ecological model for true abundance
for (i in 1:M){
N[i] ~ dpois(lambda[i])
log(lambda[i]) <- beta0[hab[i]] + beta1[hab[i]] * vegHt[i]
# Some intermediate derived quantities
critical[i] <- step(2-N[i])# yields 1 whenever N is 2 or less
z[i] <- step(N[i]-0.5) # Indicator for occupied site
# Observation model for replicated counts
for (j in 1:J){
C[i,j] ~ dbin(p[i,j], N[i])
logit(p[i,j]) <- alpha0[j] + alpha1[j] * wind[i,j]
}
}
# Derived quantities
Nocc <- sum(z[]) # Number of occupied sites among sample of M
Ntotal <- sum(N[]) # Total population size at M sites combined
Nhab[1] <- sum(N[1:33]) # Total abundance for sites in hab A
Nhab[2] <- sum(N[34:66]) # Total abundance for sites in hab B
Nhab[3] <- sum(N[67:100])# Total abundance for sites in hab C
for(k in 1:100){ # Predictions of lambda and p ...
for(level in 1:3){ # ... for each level of hab and time factors
lam.pred[k, level] <- exp(beta0[level] + beta1[level] * XvegHt[k])
logit(p.pred[k, level]) <- alpha0[level] + alpha1[level] * Xwind[k]
}
}
N.critical <- sum(critical[]) # Number of populations with critical size
}")
```

### Brief summary of the model

This is known as an “N-mixture” model in ecology. The details aren’t
really important for illustrating the mechanics of converting this model
to NIMBLE, but here is a brief summary anyway. The latent abundances
`N[i]`

at sites `i = 1...M`

are assumed to follow
a Poisson. The j-th count at the i-th site, `C[i, j]`

, is
assumed to follow a binomial with detection probability
`p[i, j]`

. The abundance at each site depends on a
habitat-specific intercept and coefficient for vegetation height, with a
log link. The detection probability for each sampling occasion depends
on a date-specific intercept and coefficient for wind speed. Kéry and
Royle concocted this as a simulated example to illustrate the
hierarchical modeling approaches for estimating abundance from count
data on repeated visits to multiple sites.

## NIMBLE version of the model code

Here is the model converted for use in NIMBLE. In this case, the only
changes to the code are to insert some missing index ranges (see
comments).

```
Section6p4_code <- nimbleCode( {
# Priors
for(k in 1:3) { # Loop over 3 levels of hab or time factors
alpha0[k] ~ dunif(-10, 10) # Detection intercepts
alpha1[k] ~ dunif(-10, 10) # Detection slopes
beta0[k] ~ dunif(-10, 10) # Abundance intercepts
beta1[k] ~ dunif(-10, 10) # Abundance slopes
}
# Likelihood
# Ecological model for true abundance
for (i in 1:M){
N[i] ~ dpois(lambda[i])
log(lambda[i]) <- beta0[hab[i]] + beta1[hab[i]] * vegHt[i]
# Some intermediate derived quantities
critical[i] <- step(2-N[i])# yields 1 whenever N is 2 or less
z[i] <- step(N[i]-0.5) # Indicator for occupied site
# Observation model for replicated counts
for (j in 1:J){
C[i,j] ~ dbin(p[i,j], N[i])
logit(p[i,j]) <- alpha0[j] + alpha1[j] * wind[i,j]
}
}
# Derived quantities; unnececssary when running for inference purpose
# NIMBLE: We have filled in indices in the next two lines.
Nocc <- sum(z[1:100]) # Number of occupied sites among sample of M
Ntotal <- sum(N[1:100]) # Total population size at M sites combined
Nhab[1] <- sum(N[1:33]) # Total abundance for sites in hab A
Nhab[2] <- sum(N[34:66]) # Total abundance for sites in hab B
Nhab[3] <- sum(N[67:100])# Total abundance for sites in hab C
for(k in 1:100){ # Predictions of lambda and p ...
for(level in 1:3){ # ... for each level of hab and time factors
lam.pred[k, level] <- exp(beta0[level] + beta1[level] * XvegHt[k])
logit(p.pred[k, level]) <- alpha0[level] + alpha1[level] * Xwind[k]
}
}
# NIMBLE: We have filled in indices in the next line.
N.critical <- sum(critical[1:100]) # Number of populations with critical size
})
```

## Simulated data

To carry this example further, we need some simulated data. Kéry and
Royle provide separate code to do this. With NIMBLE we could use the
model itself to simulate data rather than writing separate simulation
code. But for our goals here, we simply copy Kéry and Royle’s simulation
code, and we compact it somewhat:

```
# Code from Kery and Royle (2015)
# Choose sample sizes and prepare obs. data array y
set.seed(1) # So we all get same data set
M <- 100 # Number of sites
J <- 3 # Number of repeated abundance measurements
C <- matrix(NA, nrow = M, ncol = J) # to contain the observed data
# Create a covariate called vegHt
vegHt <- sort(runif(M, -1, 1)) # sort for graphical convenience
# Choose parameter values for abundance model and compute lambda
beta0 <- 0 # Log-scale intercept
beta1 <- 2 # Log-scale slope for vegHt
lambda <- exp(beta0 + beta1 * vegHt) # Expected abundance
# Draw local abundance
N <- rpois(M, lambda)
# Create a covariate called wind
wind <- array(runif(M * J, -1, 1), dim = c(M, J))
# Choose parameter values for measurement error model and compute detectability
alpha0 <- -2 # Logit-scale intercept
alpha1 <- -3 # Logit-scale slope for wind
p <- plogis(alpha0 + alpha1 * wind) # Detection probability
# Take J = 3 abundance measurements at each site
for(j in 1:J) {
C[,j] <- rbinom(M, N, p[,j])
}
# Create factors
time <- matrix(rep(as.character(1:J), M), ncol = J, byrow = TRUE)
hab <- c(rep("A", 33), rep("B", 33), rep("C", 34)) # assumes M = 100
# Bundle data
# NIMBLE: For full flexibility, we could separate this list
# into constants and data lists. For simplicity we will keep
# it as one list to be provided as the "constants" argument.
# See comments about how we would split it if desired.
win.data <- list(
## NIMBLE: C is the actual data
C = C,
## NIMBLE: Covariates can be data or constants
## If they are data, you could modify them after the model is built
wind = wind,
vegHt = vegHt,
XvegHt = seq(-1, 1,, 100), # Used only for derived quantities
Xwind = seq(-1, 1,,100), # Used only for derived quantities
## NIMBLE: The rest of these are constants, needed for model definition
## We can provide them in the same list and NIMBLE will figure it out.
M = nrow(C),
J = ncol(C),
hab = as.numeric(factor(hab))
)
```

## Initial values

Next we need to set up initial values and choose parameters to
monitor in the MCMC output. To do so we will again directly use Kéry and
Royle’s code.

```
Nst <- apply(C, 1, max)+1 # Important to give good inits for latent N
inits <- function() list(N = Nst,
alpha0 = rnorm(3),
alpha1 = rnorm(3),
beta0 = rnorm(3),
beta1 = rnorm(3))
# Parameters monitored
# could also estimate N, bayesian counterpart to BUPs before: simply add "N" to the list
params <- c("alpha0", "alpha1", "beta0", "beta1", "Nocc", "Ntotal", "Nhab", "N.critical", "lam.pred", "p.pred")
```

## Run MCMC with `nimbleMCMC`

Now we are ready to run an MCMC in nimble. We will run only one
chain, using the same settings as Kéry and Royle.

```
samples <- nimbleMCMC(
code = Section6p4_code,
constants = win.data, ## provide the combined data & constants as constants
inits = inits,
monitors = params,
niter = 22000,
nburnin = 2000,
thin = 10)
```

`## Defining model`

`## [Note] Using 'C' (given within 'constants') as data.`

`## Building model`

`## Setting data and initial values`

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

`## Checking model sizes and dimensions`

`## Checking model calculations`

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

`## running chain 1...`

```
## |-------------|-------------|-------------|-------------|
## |-------------------------------------------------------|
```

## Work with the samples

Finally we want to look at our samples. NIMBLE returns samples as a
simple matrix with named columns. There are numerous packages for
processing MCMC output. If you want to use the `coda`

package, you can convert a matrix to a coda mcmc object like this:

```
library(coda)
coda.samples <- as.mcmc(samples)
```

Alternatively, if you call `nimbleMCMC`

with the argument
`samplesAsCodaMCMC = TRUE`

, the samples will be returned as a
coda object.

To show that MCMC really happened, here is a plot of
`N.critical`

:

```
plot(jitter(samples[, "N.critical"]), xlab = "iteration", ylab = "N.critical",
main = "Number of populations with critical size",
type = "l")
```