stationary_moments: Analytic calculation of periodically stationary moments...

In jbracher/hhh4addon: Extensions to endemic-epidemic timeseries modeling from package surveillance

Analytic calculation of periodically stationary moments implied by a hhh4-model

Description

Returns the mean vector and covariance matrix of the periodically stationary distribution implied by an hhh4 object.

Usage

stationary_moments(
  hhh4Obj,
  start = 1,
  n_seasons = 1,
  return_Sigma = FALSE,
  return_cov_array = FALSE,
  return_mu_decomposed = FALSE,
  return_M = FALSE,
  max.iter = 10,
  tolerance = 1e-05
)

Arguments

hhh4Obj	hhh4 object for which to calculate stationary moments
start	start of the season
n_seasons	number of
return_Sigma	logical: return entire variance/covariance matrix of the prediction; can take a lot of storage
return_cov_array	logical: return an array containing week-wise covariance matrices
return_mu_decomposed	logical: return an array containing a decomposition of stationary means into the three components endemic, epi.own and epi.others.
return_M	logical: return the array M containing un-centered second moments (used internally for calculations)
max.iter	maximum number of iterations before iterative algorithm stops
tolerance	element-wise maximum tolerance (entering into termination criterion for the iterative calculation)

Value

An object of class stationary_moments_hhh4 containing the following components:

• mu_matrix A matrix containing the stationary means. Each row corresponds to a time period and each column to a unit.

• var_matrix A matrix containing the stationary variances.

• cov_array An array containing time period-wise variance-covariance matrices.

• mu_vector as mu_matrix, but flattened into a vector.

• Sigma a large covariance matrix for all elements of the prediction (corresponding to mu_vector)

• M a matrix containing stationary means and (un-centered) second moments, specifically E(c(1, X) Important in the internal calculation, accessible mainly for de-bugging purposes.

• mu_decomposed an array with the same number of rows and columns as mu_matrix, but three layers corresponding to the contributions of the three components to the means

• start the position (within a cycle) of the time period to which the first elements of mu_matrix etc. correspond (i.e. the start argument from the call of stationary_moments)

• freq the length of a cycle

• n_seasons the number of seasons covered in mu_matrix etc.

• n_units the number of units covered in the prediction

• timepoints the positions within a cycle of the timepoints covered by mu_matrix etc.

• condition NULL. Only relevant in predictive moments, just a place holder here.

• type "stationary"; to distinguish from predictive moments.

• has_temporal_structure does the object still have the original temporal structure? can be set to FALSE when aggregated using aggregate_prediction.

Examples

data("salmonella.agona")
## convert old "disProg" to new "sts" data class
salmonella <- disProg2sts(salmonella.agona)
# specify and fit model
control_salmonella <- list(end = list(f = addSeason2formula(~ 1), lag = 1),
                           ar = list(f = addSeason2formula(~ 1), lag = 1),
                           family = "NegBinM")
fit_salmonella <- hhh4(salmonella, control_salmonella)
# obtain periodically stationary moments:
stat_mom <- stationary_moments(fit_salmonella)
# plot periodically stationary means:
fanplot_stationary(stat_mom)
# add paths of the six seasons in the data set:
for(i in 0:5){
 lines(1:52/52, salmonella@observed[(i*52 + 1):((i + 1)*52)], col = "blue")
}
legend("topleft", col = "blue", lty = 1, legend = "observed seasons")

jbracher/hhh4addon documentation built on Feb. 16, 2024, 1:45 a.m.