RegressionDLM.R

#####################################
# Simulate Data From Regression DLM #
#####################################

regression_dlm = function(n = 6 * 24, psi, X) {
  theta = matrix(NA_real_, ncol = ncol(X), nrow = n)
  y = numeric(n)
  V = psi[1]
  W = diag(psi[2:3])
  theta[1,] = rnorm(2)
  FF = X
  y[1] = t(FF[1,]) %*% theta[1,] + rnorm(1, 0, sqrt(V))
  
  for (t in 2:n) {
    theta[t,] = theta[t-1,] + MASS::mvrnorm(1, mu = rep(0, ncol(W)), Sigma = sqrt(W))
    y[t] = t(FF[t,]) %*% theta[t,] + rnorm(1, 0, sqrt(V))
  }
  cbind(time = 1:n, state = theta, latency = y, covariates = X) 
}

arrival_rate = rpois(6*24, lambda = 5)
nodes = rep(10, 3*24), rep(20, 3*24)

data = regression_dlm(psi = c(1.0, 4.0, 3.0), X = matrix(c(arrival_rate, nodes), ncol = 2)) %>%
  as_data_frame()
  
names(data) = c("time", "theta1", "theta2", "latency", "arrival_rate", "nodes")

data %>%
  select(-contains("theta")) %>%
  gather(key, value, -time) %>%
  ggplot(aes(x = time, y = value, colour = key)) +
  geom_line() +
  facet_wrap(~key, ncol = 1, scales = "free_y")