Lsn Model Comparisons

library(knitr)
library(nimble)
library(sde)
library(ggplot2)
library(tidyr)
opts_chunk$set(dev = 'png', fig.width = 5, fig.height = 5, results = 'hide') Stick with SDE example as a reference point: set.seed(123) d <- expression(0.5 * (10-x)) s <- expression(1) data <- as.data.frame(sde.sim(X0=6,drift=d, sigma=s, T=20, N=100)) sigma.x not provided, attempting symbolic derivation. ggplot(data) + geom_line(aes(seq_along(x),x)) N <- length(data$x)

LSN version

Modify the LSN model to explicitly model the changing parameter as a hidden, stochastic variable

lsn <- nimbleCode({
theta ~ dunif(1e-10, 100.0)
sigma_x ~ dunif(1e-10, 100.0)
sigma_y ~ dunif(1e-10, 100.0)
m ~ dunif(-1e2, 1e2)
x[1] ~ dunif(0, 100)
y[1] ~ dunif(0, 100)

for(i in 1:(N-1)){
mu_x[i] <- x[i] + y[i] * (theta - x[i])
x[i+1] ~ dnorm(mu_x[i], sd = sigma_x)
mu_y[i] <- y[i] + m * t[i]
y[i+1] ~ dnorm(mu_y[i], sd = sigma_y)
}
})

Constants in the model definition are the length of the dataset, $$N$$ and the time points of the sample. Note we’ve made time explicit, we’ll assume uniform spacing here.

constants <- list(N = N, t = 1:N)

Initial values for the parameters

inits <- list(theta = 6, m = 0, sigma_x = 1, sigma_y = 1, y = rep(1,N))

and here we go:

Rmodel <- nimbleModel(code = lsn,
constants = constants,
data = data,
inits = inits)
Cmodel <- compileNimble(Rmodel)
mcmcspec <- configureMCMC(Rmodel, print=TRUE,thin=2e2)
Rmcmc <- buildMCMC(mcmcspec)
Cmcmc <- compileNimble(Rmcmc, project = Cmodel)
Cmcmc$run(1e6) NULL and examine results samples <- as.data.frame(as.matrix(Cmcmc$mvSamples))
dim(samples)
[1] 5000  206
samples <- samples[,1:4]
long <- gather(samples)
apply(samples, 2, mean)
            m       sigma_x       sigma_y         theta
-1.675333e-05  3.875174e-01  4.066872e-02  1.022867e+01 
ggplot(long) +
geom_line(aes(seq_along(value), value)) +
facet_wrap(~key, scale='free')
ggplot(long) +
geom_density(aes(value)) +
facet_wrap(~key, scale='free')
sessionInfo()
R version 3.1.3 RC (2015-03-06 r67947)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Debian GNU/Linux 8 (jessie)

locale:
[1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8       LC_NAME=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats4    splines   methods   stats     graphics  grDevices
[7] utils     datasets  base

other attached packages:
[1] tidyr_0.2.0   ggplot2_1.0.0 sde_2.0.13    zoo_1.7-11
[5] fda_2.4.4     Matrix_1.1-5  MASS_7.3-39   nimble_0.3-1
[9] yaml_2.1.13   knitr_1.9

loaded via a namespace (and not attached):
[1] codetools_0.2-11 colorspace_1.2-6 digest_0.6.8
[4] evaluate_0.5.5   formatR_1.0      grid_3.1.3
[7] gtable_0.1.2     igraph_0.7.1     labeling_0.3
[10] lattice_0.20-30  munsell_0.4.2    plyr_1.8.1
[13] proto_0.3-10     Rcpp_0.11.5      reshape2_1.4.1
[16] scales_0.2.4     stringr_0.6.2    tools_3.1.3