fdlm: MCMC Sampling Algorithm for the Functional Dynamic Linear...
In drkowal/dfosr: Dynamic Function-on-Scalars Regression

Description Usage Arguments Value Note Examples

Runs the MCMC for the functional dynamic linear model (with no predictor variables). The dynamic factors are modeled using an AR(1) model.

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fdlm(Y, tau, K = NULL, nsave = 1000, nburn = 1000, nskip = 3,
  mcmc_params = list("beta", "fk"), use_obs_SV = FALSE, X_Tp1 = 1,
  includeBasisInnovation = FALSE, Con_mat = NULL)

`Y`	the `T x m` data observation matrix, where `T` is the number of time points and `m` is the number of observation points (`NA`s allowed)
`tau`	the `m x d` matrix of coordinates of observation points
`K`	the number of factors; if NULL, use SVD-based proportion of variability explained
`nsave`	number of MCMC iterations to record
`nburn`	number of MCMC iterations to discard (burin-in)
`nskip`	number of MCMC iterations to skip between saving iterations, i.e., save every (nskip + 1)th draw
`mcmc_params`	named list of parameters for which we store the MCMC output; must be one or more of "beta" (dynamic factors) "fk" (loading curves) "mu_k" (intercept) "sigma_et" (observation error SD; possibly dynamic) "Yhat" (fitted values) "Ypred" (posterior predictive values) "Yfore" (one-step forecast; includes the estimate and the distribution)
`use_obs_SV`	logical; when TRUE, include a stochastic volatility model for the observation error variance
`X_Tp1`	the `p x 1` matrix of predictors at the forecasting time point `T + 1`
`includeBasisInnovation`	logical; when TRUE, include an iid basis coefficient term for residual correlation (i.e., the idiosyncratic error term for a factor model on the full basis matrix)
`Con_mat`	a `Jc x m` matrix of constraints for the loading curves such that `Con_mat*fk = 0` for each loading curve `fk`; default is NULL for no constraints.

A named list of the nsave MCMC samples for the parameters named in mcmc_params

If Tm is large, then storing all posterior samples for Yhat or Ypred, which are nsave x T x m, may be inefficient

# Simulate some data (w/o predictors):
sim_data = simulate_dfosr(T = 100, m = 20,
                          p_0 = 0, p_1 = 0)
Y = sim_data$Y; tau = sim_data$tau
T = nrow(Y); m = ncol(Y); # Dimensions

# Run the MCMC w/ K = 6:
out = fdlm(Y = Y, tau = tau, K = 6,
           mcmc_params = list("beta", "fk", "Yhat", "Ypred"))

# Plot the factors:
plot_factors(post_beta = out$beta)

# Plot the loading curves:
plot_flc(post_fk = out$fk, tau = tau)

# Plot a fitted value w/ posterior predictive credible intervals:
i = sample(1:T, 1); # Select a random time i
plot_fitted(y = Y[i,],
            mu = colMeans(out$Yhat)[i,],
            postY = out$Ypred[,i,],
            y_true = sim_data$Y_true[i,],
            t01 = tau)