Particle Filter Approximation of Log-Likelihood

Approximates the log-likelihood of a state space model using particle filters. This function is useful for nonlinear/non-Gaussian models where the exact Kalman filter likelihood is not available.

Usage

ll_pfilter(
  model,
  y,
  N_particles = 1000,
  filter_type = c("sir", "apf", "optimal"),
  resampling = c("systematic", "multinomial", "stratified"),
  ess_threshold = 0.5,
  N_runs = 10,
  ...
)

# S3 method for class 'stspmod'
ll_pfilter(
  model,
  y,
  N_particles = 1000,
  filter_type = c("sir", "apf", "optimal"),
  resampling = c("systematic", "multinomial", "stratified"),
  ess_threshold = 0.5,
  N_runs = 10,
  ...
)

Arguments

model

stspmod() object, which represents the state space model. For nonlinear models, additional parameters may be required.

y

sample, i.e. an \((N,m)\) dimensional matrix, or a "time series" object (i.e. as.matrix(y) should return an \((N,m)\)-dimensional numeric matrix). Missing values (NA, NaN and Inf) are not supported.

N_particles

Number of particles to use (default: 1000).

filter_type

Type of particle filter to use for likelihood approximation. Options: "sir" (default), "apf".

resampling

Resampling method: "multinomial", "systematic" (default), or "stratified".

ess_threshold

Effective sample size threshold for triggering resampling (default: 0.5). Resampling occurs when ESS < ess_threshold * N_particles.

N_runs

Number of independent particle filter runs to average over (default: 10). Averaging reduces the variance of the likelihood estimator.

...

Additional arguments passed to filter implementations.

Value

Particle filter approximation of the log-likelihood (scaled by \(1/N\)).

See also

ll_kf() for exact Kalman filter likelihood (linear Gaussian models), pf() for particle filtering.

Examples

# Linear Gaussian example: compare particle filter likelihood with Kalman filter
set.seed(123)
s = 2
m = 1
n = m
n.obs = 100

tmpl = tmpl_stsp_full(m, n, s, sigma_L = "chol")
model = r_model(tmpl, bpoles = 1, sd = 0.5)
data = sim(model, n.obs = n.obs)

# Kalman filter likelihood (exact)
ll_exact = ll_kf(model, data$y)

# Particle filter likelihood approximation
ll_approx = ll_pfilter(model, data$y, N_particles = 1000, N_runs = 5)

# Compare (should be close for linear Gaussian model with enough particles)
cat("Exact (Kalman):", ll_exact, "\n")
#> Exact (Kalman): -0.2533242 
cat("Approx (PF):", ll_approx, "\n")
#> Approx (PF): -33.54036 
cat("Difference:", ll_approx - ll_exact, "\n")
#> Difference: -33.28704