Estimate model parameters (Bayesian or maximum likelihood)

Estimates any subset of structural parameters and shock standard deviations from data, using the Kalman-filter likelihood of the solved model. method = "bayes" finds the posterior mode (in transformed, unconstrained space), seeds an adaptive random-walk Metropolis sampler with the inverse Hessian, and returns posterior draws with split R-hat and effective-sample-size diagnostics. method = "mle" uses the same machinery with flat priors on the declared supports.

Usage

qpm_estimate(
  model,
  data,
  priors,
  observables = NULL,
  measurement_error = 0,
  kappa = 1e+06,
  method = c("bayes", "mle"),
  iter = 4000,
  burn = floor(iter/2),
  chains = 2,
  thin = 1,
  seed = NULL,
  verbose = TRUE
)

# S3 method for class 'qpm_estimate'
coef(object, type = c("mean", "mode", "median"), ...)

Arguments

model: A qpm_model.
data: Data frame in levels (as for qpm_filter()).
priors: A priors() declaration. Names are structural parameters or shock names (meaning that shock's sd). Required for method = "bayes"; for "mle" it supplies supports (and is otherwise ignored).
observables, measurement_error, kappa: Passed to the filter.
method: "bayes" (default) or "mle".
iter: MCMC iterations per chain (including burn-in).
burn: Burn-in iterations (default iter/2).
chains: Number of chains (run sequentially).
thin: Keep every thin-th post-burn draw.
seed: Optional RNG seed. The previous state of the random number generator is restored on exit, so a seeded call does not disturb the caller's random stream.
verbose: Report progress with message().
object: A qpm_estimate.
type: Point estimate: posterior "mean", "mode", or "median".
...: Unused.

Value

An object of class qpm_estimate: posterior draws (natural units), the mode, acceptance rate, split R-hat and effective sample sizes, and the originating model/data. Use coef() to extract point estimates and apply_estimate() to recalibrate the model.

Details

Draws that violate Blanchard-Kahn (indeterminacy or explosiveness) receive zero posterior weight — the usual truncation of the prior to the determinacy region. Everything without a prior stays calibrated at its current value.

Examples

# \donttest{
m <- qpm_model(variables = vars(x = "x"), shocks = shocks(e),
               equations = eqs(x ~ rho * x[-1] + e),
               params = list(rho = 0.5))
obs <- simulate(qpm_solve(qpm_calibrate(m, rho = 0.8)), nsim = 100, seed = 1)
est <- qpm_estimate(m, obs, priors(rho = beta(0.5, 0.2), e = invgamma(1, 0.3)),
                    iter = 300, chains = 2, seed = 2, verbose = FALSE)
est
#> <qpm_estimate> Bayesian (adaptive RWM) - 2 parameters, 2 chains x 300 draws (burn 150, acceptance 0.29)
#>   log-posterior at mode: -130.68
#>   param      prior                  mode     mean       5%      95%  R-hat    ESS learned
#>   rho        beta(0.5, 0.2)        0.723    0.717    0.645    0.799   1.00     56 yes
#>   e          invgamma(1, 0.3)      0.894    0.910    0.807    1.041   1.01     47 yes
#>   'learned' compares posterior to prior sd (yes < 0.5 < some < 0.9 < little)
# }