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‎r/example1-lgss.R‎

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##############################################################################
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# State estimation in a LGSS model using particle and Kalman filters
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################
@@ -105,7 +105,7 @@ for (ii in 1:length(gridN)) {
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particleFilter(y, c(phi, sigmav, sigmae), gridN[ii], initialState)
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pfEstimate <- pfEstimate$xHatFiltered
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kfEstimate <- outputKF$xHatFiltered[-(T + 1)]
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logBiasMSE[ii, 1] <- log(mean(abs(pfEstimate - kfEstimate)))
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logBiasMSE[ii, 2] <- log(mean((pfEstimate - kfEstimate) ^ 2))
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}
@@ -158,7 +158,7 @@ if (savePlotToFile) {
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# Print a table (no. particles, log-bias, log-mse)
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print(t(rbind(gridN, t(logBiasMSE))))
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# gridN
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# gridN
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# [1,] 10 -3.696997 -6.938594
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# [2,] 20 -3.964671 -7.493297
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# [3,] 50 -4.567552 -8.718346

‎r/example2-lgss.R‎

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##############################################################################
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# Parameter estimation using particle Metropolis-Hastings in a LGSS model.
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################

‎r/example3-sv.R‎

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##############################################################################
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# Parameter estimation using particle Metropolis-Hastings in a SV model
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################

‎r/example4-sv.R‎

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# Parameter estimation using particle Metropolis-Hastings in a SV
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# with a proposal adapted from a pilot run.
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################

‎r/example5-sv.R‎

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# Parameter estimation using particle Metropolis-Hastings in a reparameterised version of a
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# stochastic volatility model with a proposal adapted from a pilot run.
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################

‎r/extra-code-for-tutorial/example1-lgss-plotData.R‎

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##############################################################################
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# Generates and plots data from a LGSS model.
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################

‎r/extra-code-for-tutorial/example2-lgss-varyingT.R‎

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##############################################################################
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# Runs the particle Metropolis-Hastings algorithm from different number
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# Runs the particle Metropolis-Hastings algorithm from different number
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# of observations generated from a LGSS model.
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################
@@ -44,7 +44,7 @@ if (loadSavedWorkspace) {
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load("../savedWorkspaces/example2-lgss-varyingT.RData")
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} else {
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for (i in 1:length(TT)) {
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set.seed(10)
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data <- generateData(c(phi, sigmav, sigmae), TT[i], initialState)
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res <-
@@ -58,7 +58,7 @@ if (loadSavedWorkspace) {
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noIterations,
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stepSize
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)
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Tmean[i] <- mean(res[noBurnInIterations:noIterations])
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Tvar[i] <- var(res[noBurnInIterations:noIterations])
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}

‎r/extra-code-for-tutorial/example4-sv-plotProposals.R‎

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##############################################################################
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# Ugly code to plot the estimate of the posterior distribution and the
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# proposal distribution adapted from a pilot run of particle
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# Ugly code to plot the estimate of the posterior distribution and the
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# proposal distribution adapted from a pilot run of particle
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# Metropolis-Hastings.
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################
@@ -15,7 +15,7 @@ library("mvtnorm")
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# Save plot to file
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savePlotToFile <- FALSE
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# Load the run
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# Load the run
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load("../savedWorkspaces/example3-sv.RData")
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##############################################################################
@@ -85,7 +85,7 @@ for (ii in 1:length(gridth2)) {
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##############################################################################
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# Evaluate the proposal distribution over the grid centered at the
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# Evaluate the proposal distribution over the grid centered at the
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# posterior mean
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##############################################################################
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‎r/extra-code-for-tutorial/example4-sv-varyingN.R‎

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# Example of particle Metropolis-Hastings in a stochastic volatility model
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# The effect on mixing while varying N.
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################
@@ -58,19 +58,19 @@ if (!loadSavedWorkspace) {
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for (k in 1:length(noParticles)) {
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# Save the current time
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ptm <- proc.time()
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for (i in 1:noSimulations) {
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# Run the particle filter
6464
res <- particleFilterSVmodel(y, theta, noParticles[k])
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# Save the log-Likelihood estimate
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logLikelihoodEstimates[k, i] <- res$logLikelihood
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}
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# Compute the variance of the log-likelihood and computational time per sample
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logLikelihoodVariance[k] <- var(logLikelihoodEstimates[k, ])
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computationalTimePerSample[k] <- (proc.time() - ptm)[3] / noSimulations
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# Print to screen
7575
print(paste(paste(paste(paste("Simulation: ", k, sep = ""), " of ", sep = ""), length(noParticles), sep = ""), " completed.", sep = ""))
7676
print(paste(paste(paste(paste("No. particles: ", noParticles[k], sep = ""), " requires ", sep = ""), computationalTimePerSample[k], sep = ""), " seconds for computing one sample.", sep = ""))
@@ -104,21 +104,21 @@ if (loadSavedWorkspace) {
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resTheta <- array(0, dim = c(length(noParticles), noIterations - noBurnInIterations + 1, 3))
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computationalTimePerIteration <- rep(0, length(noParticles))
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acceptProbability <- rep(0, length(noParticles))
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for (k in 1:length(noParticles)) {
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# Save the current time
110110
ptm <- proc.time()
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# Run the PMH algorithm
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res <- particleMetropolisHastingsSVmodel(y, initialTheta, noParticles[k], noIterations, stepSize = proposals[k, ,])
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# Save the parameter trace
116116
resTheta[k, ,] <- res$theta[noBurnInIterations:noIterations,]
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# Compute acceptance probability and computational time per sample
119-
computationalTimePerIteration[k] <- (proc.time() - ptm)[3] / noIterations
119+
computationalTimePerIteration[k] <- (proc.time() - ptm)[3] / noIterations
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acceptProbability[k] <- mean(res$proposedThetaAccepted[noBurnInIterations:noIterations])
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# Print to screen
123123
print(paste(paste(paste(paste("Simulation: ", k, sep = ""), " of ", sep = ""), length(noParticles), sep = ""), " completed.", sep = ""))
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}
@@ -134,7 +134,7 @@ for (k in 1:length(noParticles)) {
134134
acf_mu <- acf(resTheta[k, , 1], plot = FALSE, lag.max = 250)
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acf_phi <- acf(resTheta[k, , 2], plot = FALSE, lag.max = 250)
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acf_sigmav <- acf(resTheta[k, , 3], plot = FALSE, lag.max = 250)
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resThetaIACT[k, ] <- 1 + 2 * c(sum(acf_mu$acf), sum(acf_phi$acf), sum(acf_sigmav$acf))
139139
resThetaIACTperSecond[k, ] <- resThetaIACT[k, ] / computationalTimePerIteration[k]
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}
@@ -148,7 +148,7 @@ print(table)
148148
##############################################################################
149149
if (tuneProposals) {
150150
proposals <- array(0, dim = c(length(noParticles), 3, 3))
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for (k in 1:length(noParticles)) {
153153
proposals[k, , ] <- cov(resTheta[k, , ]) * 2.562^2 / 3
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}

‎r/helpers/dataGeneration.R‎

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##############################################################################
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# Generating data from a LGSS model
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#
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# Johan Dahlin <liu (at) johandahlin.com.nospam>
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# Johan Dahlin <uni (at) johandahlin.com.nospam>
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# Documentation at https://github.com/compops/pmh-tutorial
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# Published under GNU General Public License
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##############################################################################
8-
generateData <- function(theta, noObservations, initialState)
8+
generateData <- function(theta, noObservations, initialState)
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{
10-
phi <- theta[1]
10+
phi <- theta[1]
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sigmav <- theta[2]
1212
sigmae <- theta[3]
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state <- matrix(0, nrow = noObservations + 1, ncol = 1)
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observation <- matrix(0, nrow = noObservations + 1, ncol = 1)
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1717
state[1] <- initialState
1818
observation[1] <- NA
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for (t in 2:(noObservations + 1)) {
2121
state[t] <- phi * state[t - 1] + sigmav * rnorm(1)
2222
observation[t] <- state[t] + sigmae * rnorm(1)
2323
}
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list(x = state, y = observation)
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}

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