particleMetropolisHastings: Particle Metropolis-Hastings algorithm for a linear Gaussian...
In pmhtutorial: Minimal Working Examples for Particle Metropolis-Hastings

Description Usage Arguments Value Note Author(s) References Examples

Estimates the parameter posterior for phi a linear Gaussian state space model of the form x_{t} = φ x_{t-1} + σ_v v_t and y_t = x_t + σ_e e_t , where v_t and e_t denote independent standard Gaussian random variables, i.e.N(0,1).

1 2	particleMetropolisHastings(y, initialPhi, sigmav, sigmae, noParticles, initialState, noIterations, stepSize)

`y`	Observations from the model for t=1,...,T.
`initialPhi`	The mean of the log-volatility process μ.
`sigmav`	The standard deviation of the state process σ_v.
`sigmae`	The standard deviation of the observation process σ_e.
`noParticles`	The number of particles to use in the filter.
`initialState`	The inital state.
`noIterations`	The number of iterations in the PMH algorithm.
`stepSize`	The standard deviation of the Gaussian random walk proposal for φ.

The trace of the Markov chain exploring the marginal posterior for φ.

See Section 4 in the reference for more details.

Johan Dahlin uni@johandahlin.com

Dahlin, J. & Schon, T. B. "Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models." Journal of Statistical Software, Code Snippets, 88(2): 1–41, 2019.

  # Generates 100 observations from a linear state space model with
  # (phi, sigma_e, sigma_v) = (0.5, 1.0, 0.1) and zero initial state.
  theta <- c(0.5, 1.0, 0.1)
  d <- generateData(theta, noObservations=100, initialState=0.0) 

  # Estimate the marginal posterior for phi
  pmhOutput <- particleMetropolisHastings(d$y,
    initialPhi=0.1, sigmav=1.0, sigmae=0.1, noParticles=50, 
    initialState=0.0, noIterations=1000, stepSize=0.10)

  # Plot the estimate
  nbins <- floor(sqrt(1000))
  par(mfrow=c(1, 1))
  hist(pmhOutput, breaks=nbins, main="", xlab=expression(phi), 
    ylab="marginal posterior", freq=FALSE, col="#7570B3")