This post looks at the autocorrelation in a simple DLM when using JAGS, which samples each state individually, and FFBS, which samples the states jointly.
This is put within the context of a local level model with unknown observation and evolution variance.
Simulate the data
require ( methods , quietly = TRUE )
require ( dlm , quietly = TRUE )
##
## Attaching package: 'dlm'
## The following object is masked from 'package:ggplot2':
##
## %+%
require ( rjags , quietly = TRUE )
## Warning in library(package, lib.loc = lib.loc, character.only = TRUE,
## logical.return = TRUE, : there is no package called 'rjags'
# Simulate data
ll = dlmModPoly ( 1 , dV = 1 , dW = .01 , m0 = 0 , C0 = 1 )
o = dlmForecast ( ll , 100 , sampleNew = 1 )
Fit the model using JAGS (the model looks terrible, but it should work).
jags_ll = "
model {
for (i in 2:n) {
y[i1] ~ dnorm(theta[i], tauV)
theta[i] ~ dnorm(theta[i1], tauW)
}
theta[1] ~ dnorm(0,1)
tauV ~ dgamma(1,1)
tauW ~ dgamma(1,1)
}
"
dat = list ( y = as.numeric ( o $ newObs [[ 1 ]]))
dat $ n = length ( dat $ y ) +1
m = jags.model ( textConnection ( jags_ll ), dat ,
n.adapt = 2000 )
## Error in jags.model(textConnection(jags_ll), dat, n.adapt = 2000): could not find function "jags.model"
res = coda.samples ( m , c ( "tauV" , "tauW" , "theta" ), n.iter = 2000 )
## Error in coda.samples(m, c("tauV", "tauW", "theta"), n.iter = 2000): could not find function "coda.samples"
Fit the model using the dlm package in R.
joint = dlmGibbsDIG ( o $ newObs [[ 1 ]], ll ,
a.y = 1 , b.y = 1 ,
a.theta = 1 , b.theta = 1 ,
n.sample = 1000 , thin = 1 )
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Plot traceplots and autocorrelation for the middle state.
par ( mfrow = c ( 2 , 2 ))
plot ( as.numeric ( res [[ 1 ]][ 1001 : 2000 , 52 ]), type = "l" )
## Error in plot(as.numeric(res[[1]][1001:2000, 52]), type = "l"): object 'res' not found
acf ( res [[ 1 ]][, 52 ])
## Error in as.ts(x): object 'res' not found
plot ( joint $ theta [ 52 , 1 ,], type = "l" )
acf ( joint $ theta [ 52 , 1 ,])
The elephant in the room here is in the implementation since the JAGS code runs quite a bit faster than the dlm code.
Of course, the dlm code is written to handle much more complicated DLMs.
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