Summarise the implied prior on a time-varying coefficient path

Draws ndraws sample paths of length n_periods from the dynamic_beta prior (given a kind, AR(1) hyperparameters, and an inverse-gamma on the innovation variance) and reports the implied distribution of common summary statistics: maximum absolute first difference, roughness (sum of squared first differences), path range, and correlation with time. Use this before fitting to confirm that your prior is loose / tight enough.

Usage

dynamic_beta_prior_summary(
  n_periods = 10L,
  ndraws = 5000L,
  kind = c("ar1", "rw1", "rw2", "matern32"),
  rho_mean = 0.8,
  rho_sd = 0.15,
  rho_lower = 0,
  rho_upper = 0.999,
  sigma_shape = 2,
  sigma_scale = 1,
  matern32_length_scale = 2,
  threshold = 1,
  seed = NULL
)

Arguments

n_periods: Length of the path (default 10).
ndraws: Number of paths to draw (default 5000).
kind: One of "ar1", "rw1", "rw2", "matern32". Default "ar1". For "matern32" the path is drawn from a continuous-time Matérn-3/2 GP with length scale matern32_length_scale and marginal variance \(\sigma_\beta^2\).
rho_mean, rho_sd: Prior mean/SD on \(\rho\) (AR(1) only). Used to parameterise a Beta prior on the standardised \(\rho\).
rho_lower, rho_upper: Truncation bounds (AR(1) only). Default [0, 0.999].
sigma_shape, sigma_scale: Inverse-Gamma shape / scale on \(\sigma_\beta^2\). Defaults shape = 2, scale = 1.
matern32_length_scale: Length scale for the Matérn-3/2 covariance (kind = "matern32" only). Default 2.
threshold: Cutoff for the prob_max_diff_gt_threshold summary. Default 1.
seed: Optional integer seed for reproducibility.

Value

A list with components:

summary: Data frame with quantile rows for max-first-diff, roughness, path range, trend correlation.
prob_max_diff_gt_threshold: Empirical probability that the maximum absolute first difference exceeds threshold.
rho: Length ndraws vector of sampled rho values (NA for kinds with fixed rho).
sigma: Length ndraws vector of sampled sigma values.
paths: ndraws x n_periods matrix of sample paths.

Details

For kind = "ar1", rho_mean/rho_sd are translated to a Beta prior on the standardised \((\rho - \rho_{lower}) / (\rho_{upper} - \rho_{lower})\). For kind = "rw1", \(\rho = 1\) is fixed and only \(\sigma_\beta^2\) is sampled. For kind = "rw2", the second-difference variance is sampled and the first two values use a diffuse \(N(0, 10)\) initial prior.

Examples

# \donttest{
# Default prior: AR(1) with rho_mean = 0.8, rho_sd = 0.15
s <- dynamic_beta_prior_summary(n_periods = 10, ndraws = 2000, seed = 1)
s$summary
#>             quantity        q05        q50        q95
#> 1 max_abs_first_diff  0.7215172 1.46787811  3.7138105
#> 2          roughness  1.4113939 5.56455715 31.4268861
#> 3              range  1.1631870 2.62820813  6.6322426
#> 4          trend_cor -0.8732470 0.01310171  0.8807169
# what's the probability that consecutive beta_t differ by more than 1?
s$prob_max_diff_gt_threshold
#> [1] 0.799

# Tighter prior on innovation variance
s_tight <- dynamic_beta_prior_summary(sigma_scale = 0.1, seed = 1)
s_tight$summary
#>             quantity        q05        q50       q95
#> 1 max_abs_first_diff  0.2176577 0.46198529 1.1278813
#> 2          roughness  0.1372637 0.55602950 3.0626640
#> 3              range  0.3659379 0.82262847 2.0530328
#> 4          trend_cor -0.8787253 0.02435639 0.8788859
# }