Precompute shape of posterior distribution for epsilon

Usage

get_shape_epsilon(incid, lambda, priors, t_min = 2L, t_max = nrow(incid))

Arguments

incid: a multidimensional array containing values of the (local) incidence for each time step (1st dimension), location (2nd dimension) and pathogen/strain/variant (3rd dimension)
lambda: a multidimensional array containing values of the overall infectivity for each time step (1st dimension), location (2nd dimension) and pathogen/strain/variant (3rd dimension). The overall infectivity for a given location and pathogen/strain/variant represents the sum of the incidence for that location and that pathogen/strain/variant at all previous time steps, weighted by the current infectivity of those past incident cases. It can be calculated from the incidence incid and the distribution of the serial interval using function compute_lambda()
priors: a list of prior parameters (shape and scale of a gamma distribution) for epsilon and R; can be obtained from the function default_priors(). The prior for R is assumed to be the same for all time steps and all locations
t_min: an integer > 1 giving the minimum time step to consider in the estimation. Default value is 2 (as the estimation is conditional on observations at time step 1 and can therefore only start at time step 2).
t_max: an integer > t_min and <= nrow(incid) giving the maximum time step to consider in the estimation. Default value is nrow(incid).

Value

a value or vector of values of the shape of the posterior distribution of epsilon for each of the non-reference variants

Examples

n_loc <- 4 # 4 locations
n_v <- 3 # 3 strains
T <- 100 # 100 time steps
priors <- default_priors()
# constant incidence 10 per day everywhere
incid <- array(10, dim = c(T, n_loc, n_v))
incid <- process_I_multivariant(incid)
# arbitrary serial interval, same for both variants
w_v <- c(0, 0.2, 0.5, 0.3)
si_distr <- cbind(w_v, w_v, w_v)
lambda <- compute_lambda(incid, si_distr)
get_shape_epsilon(incid$local, lambda, priors)
#> [1] 3961 3961