lame (version 1.3.4)

dynamic_beta_prior_summary: Summarise the implied prior on a time-varying coefficient path

Description

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
)

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.

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.

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$summary
# what's the probability that consecutive beta_t differ by more than 1?
s$prob_max_diff_gt_threshold

# Tighter prior on innovation variance
s_tight <- dynamic_beta_prior_summary(sigma_scale = 0.1, seed = 1)
s_tight$summary
# }