Epidemic process for the Bayesian Nowcast — epidemic

Specify the latent epidemic process. Parameter slots accept a fixed numeric, a prior_class, or numeric(0) for the default prior. The log-incidence mean intercept is inherited from the likelihood (mu).

Usage

hsgp_epidemic(
  alpha = numeric(0),
  ell = numeric(0),
  gp_kernel = "matern32",
  gp_basis = "dirichlet",
  num_basis = 0,
  tmax_model = 0
)

ar1_epidemic(phi = numeric(0), sigma = numeric(0), error = numeric(0))

sir_epidemic(
  R0 = numeric(0),
  gamma = numeric(0),
  N_eff = numeric(0),
  N_pop = 10000,
  use_beta_rw_trend = TRUE
)

Arguments

alpha: HSGP GP amplitude prior (> 0).
ell: HSGP GP length-scale prior (> 0).
gp_kernel: HSGP kernel: "sq_exp", "matern32" (default), "matern52".
gp_basis: HSGP eigenbasis: "dirichlet"/"sine" (default) or "neumann"/"cosine".
num_basis: HSGP basis count; numeric(0)/0 = auto from series length.
tmax_model: HSGP time normalisation; 0 = auto (newest point at the right boundary).
phi: AR(1) autocorrelation prior in (-1, 1).
sigma: AR(1) innovation SD prior (> 0).
error: AR(1) standardised innovation prior.
R0: SIR basic reproduction number prior (> 0).
gamma: SIR recovery rate prior in (0, 1).
N_eff: SIR effective susceptible fraction prior in (0, 1).
N_pop: SIR total population (default 10000).
use_beta_rw_trend: SIR: beta follows an AR(1) walk if TRUE (default).

Value

An epidemic_process_class object.

Default priors

When a prior argument is left empty, default_priors() supplies these defaults (see also nowcast(prior_only = TRUE) to visualise them):

HSGP (hsgp_epidemic):

alpha (GP amplitude): half_normal_prior(0, 1)
ell (GP length-scale): inv_gamma_prior(3, 1)

AR(1) (ar1_epidemic):

phi (autocorrelation): std_normal_prior()
sigma (innovation SD): exponential_prior(100)
innovations: std_normal_prior()

SIR (sir_epidemic):

R0: lognormal_prior(log(2), 0.5)
gamma (recovery rate): lognormal_prior(log(1/5), 0.5)
N_eff (susceptible fraction): beta_prior(2, 5)

The log-incidence intercept comes from the likelihood (mu), defaulting to a data-informed normal_prior() centred at the log median daily count.

Examples

hsgp_epidemic()
#> HSGP(alpha, ell ; kernel = "matern32", num_basis = "auto", tmax = "auto")
hsgp_epidemic(gp_kernel = "sq_exp", num_basis = 20)
#> HSGP(alpha, ell ; kernel = "sq_exp", num_basis = "20", tmax = "auto")
ar1_epidemic(phi = 0.9)
#> AR(1)(phi = "0.9", sigma | error)
sir_epidemic(R0 = 2.5, use_beta_rw_trend = FALSE)
#> SIR(R0 = "2.5", gamma, N_eff ; N_pop = "10,000", beta_rw = "FALSE")