# Nimble Explore

A quick first exploration of NIMBLE and some questions.

library("nimble")
library("sde")

Let’s simulate from a simple OU process: $$dX = \alpha (\theta - X) dt + \sigma dB_t$$

set.seed(123)
d <- expression(0.5 * (10-x))
s <- expression(1)
data <- as.data.frame(sde.sim(X0=6,drift=d, sigma=s, T=100, N=400))
## sigma.x not provided, attempting symbolic derivation.

i.e. $$\alpha = 0.5$$, $$\theta = 10$$, $$\sigma=1$$, starting at $$X_0 = 6$$ and running for 100 time units with a dense sampling of 400 points.

Le’t now estimate a Ricker model based upon (set aside closed-form solutions to this estimate for the moment, since we’re investigating MCMC behavior here).

code <- modelCode({
K ~ dunif(0.01, 40.0)
r ~ dunif(0.01, 20.0)
sigma ~ dunif(1e-6, 100)

iQ <- 1 / (sigma * sigma)

x[1] ~ dunif(0, 10)

for(t in 1:(N-1)){
mu[t] <- log(x[t]) + r * (1 - x[t]/K)
x[t+1] ~ dlnorm(mu[t], iQ)
}
})

constants <- list(N = length(data$x)) inits <- list(K = 6, r = 1, sigma = 1) Rmodel <- nimbleModel(code=code, constants=constants, data=data, inits=inits) NIMBLE certainly makes for a nice syntax so far. Here we go now: create MCMC specification and algorithm mcmcspec <- MCMCspec(Rmodel) Rmcmc <- buildMCMC(mcmcspec) Note that we can also query some details regarding our specification (set by default) mcmcspec$getSamplers()
## [1] RW sampler;   targetNode: K,  adaptive: TRUE,  adaptInterval: 200,  scale: 1
## [2] RW sampler;   targetNode: r,  adaptive: TRUE,  adaptInterval: 200,  scale: 1
## [3] RW sampler;   targetNode: sigma,  adaptive: TRUE,  adaptInterval: 200,  scale: 1
mcmcspec$getMonitors() ## thin = 1: K, r, sigma, x Now we’re ready to compile model and MCMC algorithm Cmodel <- compileNimble(Rmodel) Cmcmc <- compileNimble(Rmcmc, project = Cmodel) Note we could have specified the Rmodel as the “project” (as shown in the example from the Nimble website), but this is more explicit. Rather convenient way to add to an existing model in this manner. And Now we can execute the MCMC algorithm in blazing fast C++ and then extract the samples Cmcmc(10000) ## NULL samples <- as.data.frame(as.matrix(nfVar(Cmcmc, 'mvSamples'))) How do these estimates compare to theory: mean(samples$K)
## [1] 10.05681
mean(samples\$r)
## [1] 0.180207

Some quick impressions:

• Strange that Rmodel call has to be repeated before we can set up a custom MCMC (nimble docs). How/when was this object altered since it was defined in the above code? Seems like this could be problematic for interpreting / reproducing results?

• What’s going on with getSamplers() and getMonitors()? Guessing these are in there just to show us what the defaults will be for our model?

• why do we assign Cmodel if it seems we don’t use it? (the compilation needs to be done but isn’t explicitly passed to the next step). Seems we can use Cmodel instead of Rmodel in the Cmcmc <- compileNimble(Rmcmc, project = Cmodel), which makes the dependency more explicit, at least that notation is more explicit. Seems like it should be possiple to omit the first compileNimble() and have the second call the compileNimble automatically if it gets an object whose class is that of Rmodel instead?

• Repeated calls to Cmcmc seem not to give the same results. Are we adding additional mcmc steps by doing this?

• Thinking an as.data.frame would be nicer than as.matrix in the nfVar mvSamples coercion.

• Don’t understand what simulate does (or why it always returns NULL?).