Simulating from a model
NIMBLE models can be used to simulate data. The steps required to do so are as follows:
- Create BUGS model code with
nimbleCode()describing the model - Build the model with
nimbleModel()providing constants and initial values for parameters needed for simulation - Identify the nodes to simulate
- Run
model$simulate()
1. Create model code
We’ll use a very simple toy hierarchical model, a basic occupancy
model from ecology. The occupancy model describes a situation where an
observer visits multiple sites multiple times, and on each site visit
records whether or not a target species is seen there. The parameters of
interest are psi, the probability that any one site is
occupied, and p, the probability of detecting the species
on any visit given that it is present. Note that the detection
probability may depend on the visit but for this simple example we make
it a constant across visits. It’s assumed that sites don’t change
occupancy status during the visiting period.
library(nimble, warn.conflicts = FALSE)## nimble version 1.1.0 is loaded.
## For more information on NIMBLE and a User Manual,
## please visit https://R-nimble.org.
##
## Note for advanced users who have written their own MCMC samplers:
## As of version 0.13.0, NIMBLE's protocol for handling posterior
## predictive nodes has changed in a way that could affect user-defined
## samplers in some situations. Please see Section 15.5.1 of the User Manual.simCode <- nimbleCode({
for (i in 1:nsite) {
z[i] ~ dbern(prob = psi) # True occupancy status
for (j in 1:nvisit) {
y[i,j] ~ dbern(z[i] * p) # Observed data
}
}
psi ~ dunif(0,1)
p ~ dunif(0,1)
})2. Build the model
We build the model object. We provide constants, in this case, number
of sites (nsite) and number of visits to each site
(nvisit). We also provide initial values for p
and psi.
simModel <- nimbleModel(code = simCode,
constants = list(nsite = 10, nvisit = 3),
inits = list(psi = 0.7, p = 0.33))## Defining model## Building model## Setting data and initial values## Running calculate on model
## [Note] Any error reports that follow may simply reflect missing values in model variables.## Checking model sizes and dimensions## [Note] This model is not fully initialized. This is not an error.
## To see which variables are not initialized, use model$initializeInfo().
## For more information on model initialization, see help(modelInitialization).Note that the message lets us know that some variables are not
initialized – in this case, all y and z nodes.
If we try to calculate the log probabilities of these nodes at this
point, we’ll get NA.
simModel$calculate('y')## [1] NA3. Identify nodes and simulate
The model$simulate() function allows you to specify
which nodes you want to simulate. Naively, we may want to go ahead and
simulate the y nodes with
simModel$simulate("y").However, since y
depends on z, which has not been simulated, we’ll just get
back a bunch of NAs again.
We could get around this by simulating z before
y. In more complicated models, it can be useful to use the
NIMBLE function model$getDependencies() to gather all nodes
needing to be simulated given the parameters we provided.
nodesToSim <- simModel$getDependencies(c("psi", "p"),
self = F, downstream = T)
nodesToSim## [1] "z[1]" "z[2]"
## [3] "z[3]" "z[4]"
## [5] "z[5]" "z[6]"
## [7] "z[7]" "z[8]"
## [9] "z[9]" "z[10]"
## [11] "lifted_z_oBi_cB_times_p_L4[1]" "lifted_z_oBi_cB_times_p_L4[2]"
## [13] "lifted_z_oBi_cB_times_p_L4[3]" "lifted_z_oBi_cB_times_p_L4[4]"
## [15] "lifted_z_oBi_cB_times_p_L4[5]" "lifted_z_oBi_cB_times_p_L4[6]"
## [17] "lifted_z_oBi_cB_times_p_L4[7]" "lifted_z_oBi_cB_times_p_L4[8]"
## [19] "lifted_z_oBi_cB_times_p_L4[9]" "lifted_z_oBi_cB_times_p_L4[10]"
## [21] "y[1, 1]" "y[1, 2]"
## [23] "y[1, 3]" "y[2, 1]"
## [25] "y[2, 2]" "y[2, 3]"
## [27] "y[3, 1]" "y[3, 2]"
## [29] "y[3, 3]" "y[4, 1]"
## [31] "y[4, 2]" "y[4, 3]"
## [33] "y[5, 1]" "y[5, 2]"
## [35] "y[5, 3]" "y[6, 1]"
## [37] "y[6, 2]" "y[6, 3]"
## [39] "y[7, 1]" "y[7, 2]"
## [41] "y[7, 3]" "y[8, 1]"
## [43] "y[8, 2]" "y[8, 3]"
## [45] "y[9, 1]" "y[9, 2]"
## [47] "y[9, 3]" "y[10, 1]"
## [49] "y[10, 2]" "y[10, 3]"By setting self = FALSE we specified that we didn’t want
to see psi or p in the return vector. By
setting downstream = TRUE we recursively looked at the
dependencies of nodes, rather than just the nodes directly dependent on
psi and p.
We successfully retrieved all z and y
nodes, as well as an internal set of nodes NIMBLE created to handle the
operation z[i] * p.
4. Simulate
simModel$simulate(nodesToSim)
simModel$y## [,1] [,2] [,3]
## [1,] 0 0 0
## [2,] 0 0 0
## [3,] 0 0 0
## [4,] 0 0 0
## [5,] 1 0 0
## [6,] 0 0 0
## [7,] 0 0 1
## [8,] 0 0 0
## [9,] 0 0 0
## [10,] 1 0 0We got values back for y!
We can also view the simulated latent state z.
simModel$z## [1] 0 0 0 0 1 1 1 0 1 1Compiled models
Note that this workflow looks the same with a compiled model:
CsimModel <- compileNimble(simModel)## Compiling
## [Note] This may take a minute.
## [Note] Use 'showCompilerOutput = TRUE' to see C++ compilation details.nodesToSim <- CsimModel$getDependencies(c("psi", "p"),
self = F, downstream = T)
CsimModel$simulate(nodesToSim)
CsimModel$y## [,1] [,2] [,3]
## [1,] 0 0 1
## [2,] 0 0 0
## [3,] 0 0 0
## [4,] 0 0 0
## [5,] 0 0 0
## [6,] 0 0 0
## [7,] 0 0 0
## [8,] 1 1 0
## [9,] 0 0 0
## [10,] 0 1 1Use simulated data in MCMC
To use a simulated dataset for MCMC, the data must be retrieved and
set so that the target node is identified as a data node type. Note that
we do not set the latent state z, which should not
be treated as data by the MCMC algorithm.
simulatedYs <- CsimModel$y
CsimModel$setData(list(y = simulatedYs))
simMCMC <- buildMCMC(CsimModel)## ===== Monitors =====
## thin = 1: p, psi
## ===== Samplers =====
## RW sampler (2)
## - psi
## - p
## binary sampler (10)
## - z[] (10 elements)
## ===== Comments =====## [Warning] No samplers assigned for 30 nodes.CsimMCMC <- compileNimble(simMCMC, project = simModel)## Compiling
## [Note] This may take a minute.
## [Note] Use 'showCompilerOutput = TRUE' to see C++ compilation details.samples <- runMCMC(CsimMCMC, niter = 10000)## running chain 1...## |-------------|-------------|-------------|-------------|
## |-------------------------------------------------------|plot(samples[ , 'psi'], type = 'l', xlab = 'iteration', ylab = expression(psi))
plot(samples[ , 'p'], type = 'l', xlab = 'iteration', ylab = expression(p))