dynamic_prior: Specify priors for a dynamic model

In DynCount: Bayesian Dynamic Models for Count Time Series

Specify priors for a dynamic model

Description

Builds the prior hyperparameters used by fit_dynamic_model(). Called with no arguments it returns weakly informative defaults.

Usage

dynamic_prior(
  var_shape = 0.01,
  var_rate = 0.01,
  df_min = 3,
  df_mean_excess = 6,
  mix_components = 2,
  mix_concentration = 1,
  mix_var_shape = 2.5,
  mix_var_rate = 0.5,
  sv_prior = NULL,
  zi_open_a = 1,
  zi_open_b = 1,
  ar_rho_mean = 0,
  ar_rho_sd = 1,
  mu_mean = 0,
  mu_sd = 1,
  init_mean = 0,
  init_var = 100
)

Arguments

var_shape	Shape of the inverse-gamma prior on the innovation variance/scale. Default 0.01.
var_rate	Rate of the inverse-gamma prior on the innovation variance/scale. Default 0.01.
df_min	Lower bound for the Student-t degrees of freedom. Default 3.
df_mean_excess	Prior mean of \nu - \code{df\_min}. Default 6.
mix_components	Number of components in the scale-mixture innovation structure. Default 2.
mix_concentration	Symmetric Dirichlet concentration for the mixture weights. Default 1.
mix_var_shape, mix_var_rate	Shape and rate of the inverse-gamma prior on the relative variance of each mixture component (used only when innovations = "mixture"). Defaults 2.5 and 0.5.
sv_prior	Optional stochvol prior specification for the stochastic-volatility innovation structure. Default NULL.
zi_open_a, zi_open_b	Beta prior parameters for the gate-open probability in zero-inflated models. Default 1 and 1.
ar_rho_mean, ar_rho_sd	Mean and standard deviation of the Gaussian prior on the AR(1) coefficient \rho (used only when latent_dynamics = "ar1"). The prior is truncated to the stationary region \rho \in (-1, 1). Defaults 0 and 1.
mu_mean, mu_sd	Mean and standard deviation of the Gaussian prior on the drift/intercept \mu (used only when include_mu = TRUE). Defaults 0 and 1.
init_mean, init_var	Mean and variance of the Gaussian prior on the initial latent state, used under both random-walk and AR(1) dynamics. Defaults 0 and 100 (a diffuse N(0, 100)).

Details

The model places a GMRF latent process on the series z_t (a log-rate for the Poisson family, a logit for the binomial family, and one additive-log-ratio series per non-baseline category for the multinomial family): either a first-order random walk (latent_dynamics = "rw") or an AR(1) process (latent_dynamics = "ar1"). The increments \varepsilon_t = z_t - \mu - \rho\, z_{t-1} (with \rho = 1 for the random walk and \mu = 0 unless a drift/intercept is included) are given one of four innovation distributions, each governed by some of the priors below.

Innovation variance (all structures). The baseline increment variance \sigma^2 (or, for the "t"/"mixture" structures, the overall scale) has an inverse-gamma prior

\sigma^2 \sim \mathrm{InvGamma}(\code{var\_shape}, \code{var\_rate}).

The default \mathrm{InvGamma}(0.01, 0.01) is weakly informative for typical increment standard deviations, but it is not scale-free. For very smooth or short series, with increment standard deviations of a few hundredths, the results can be sensitive to this prior. In that regime, check the sensitivity of the results to a smaller var_rate (which lets \sigma become smaller) and expect slower mixing, because a nearly constant latent path and a small \sigma are strongly dependent a posteriori. In the multinomial family the same prior is applied independently to every non-baseline category.

Mixture component variances (innovations = "mixture"). The relative variances of the mixture components multiply the overall scale and are given their own \mathrm{InvGamma}(\code{mix\_var\_shape}, \code{mix\_var\_rate}) prior (default \mathrm{InvGamma}(2.5, 0.5)). They are kept moderately informative on purpose, as with a vague prior an empty component would be drawn from an extremely heavy-tailed distribution and the split between the overall scale and the component variances is only weakly identified.

Student-t degrees of freedom (innovations = "t"). The degrees of freedom are modelled as \nu = \code{df\_min} + E, where E \sim \mathrm{Exp}(\mathrm{rate} = 1/\code{df\_mean\_excess}). Thus \nu \ge \code{df\_min} and its prior mean is \code{df\_min} + \code{df\_mean\_excess}. Large \nu approaches the Gaussian case.

Scale mixture (innovations = "mixture"). The mixture uses mix_components variance components, each with an \mathrm{InvGamma}(\code{mix\_var\_shape}, \code{mix\_var\_rate}) prior (see above), and symmetric Dirichlet weights with concentration mix_concentration.

Stochastic volatility (innovations = "sv"). The log-variance h_t of the increments follows h_t = \mu_h + \phi (h_{t-1} - \mu_h) + \sigma_h \eta_t, and its priors are delegated to stochvol. Pass a prior specification created with stochvol::specify_priors() via sv_prior, or leave it NULL to use the stochvol defaults.

Zero inflation (zeros = "inflated"). The probability that the observation "gate" is open (i.e. that a zero is an ordinary sampling zero rather than a structural zero) has a \mathrm{Beta}(\code{zi\_open\_a}, \code{zi\_open\_b}) prior. The default Beta(1, 1) is uniform.

AR(1) coefficient (latent_dynamics = "ar1"). When the latent state follows z_t = \mu + \rho\, z_{t-1} + \varepsilon_t, the coefficient \rho is given a Gaussian prior \rho \sim \mathrm{N}(\code{ar\_rho\_mean}, \code{ar\_rho\_sd}^2), truncated to the stationary region \rho \in (-1, 1). AR(1) always carries an intercept (include_mu = TRUE). Under latent_dynamics = "rw" the coefficient is fixed at \rho = 1 and this prior is unused.

Drift / intercept (include_mu = TRUE). A scalar \mu in the state equation z_t = \mu + \rho\, z_{t-1} + \varepsilon_t: a drift under the random walk (\rho = 1) and an intercept under AR(1) (where it is always enabled). It is given a Gaussian prior \mu \sim \mathrm{N}(\code{mu\_mean}, \code{mu\_sd}^2). With include_mu = FALSE (random walk only), \mu = 0 and is not sampled.

Initial state. A proper, fixed \mathrm{N}(\code{init\_mean}, \code{init\_var}) prior (default N(0, 100)) anchors the otherwise-improper GMRF on the first latent state, under both "rw" and "ar1" dynamics. With the diffuse default the initial state is effectively determined by the data.

Value

An object of class "dynamic_prior": a named list of hyperparameters.

See Also

fit_dynamic_model()

Examples

# Defaults
dynamic_prior()

# An informative variance prior and heavier-tailed t innovations
dynamic_prior(var_shape = 2.5, var_rate = 0.5, df_min = 2, df_mean_excess = 3)

DynCount documentation built on Sept. 28, 2026, 5:10 p.m.