Update coefficient vector

Update coefficient vector

Usage

update_coefficient(mu_beta_0, Sigma_beta_0_inv, XSigX, XSigU)

Arguments

mu_beta_0

[numeric(P)]
The prior mean for the coefficient vector,

Sigma_beta_0_inv

[matrix(P, P)]
The prior precision for the coefficient vector.

XSigX

[matrix(P, P)]
The matrix \(\sum_{n=1}^N X_n'\Sigma^{-1}X_n\).

XSigU

[numeric(P)]
The vector \(\sum_{n=1}^N X_n'\Sigma^{-1}U_n\).

Value

An update for the coefficient vector.

Examples

beta_true <- matrix(c(-1, 1), ncol = 1)
Sigma <- matrix(c(1, 0.5, 0.2, 0.5, 1, 0.2, 0.2, 0.2, 2), ncol = 3)
N <- 100
X <- replicate(N, matrix(rnorm(6), ncol = 2), simplify = FALSE)
eps <- replicate(
  N, oeli::rmvnorm(n = 1, mean = c(0, 0, 0), Sigma = Sigma),
  simplify = FALSE
)
U <- mapply(
  function(X, eps) X %*% beta_true + eps, X, eps, SIMPLIFY = FALSE
)
mu_beta_0 <- c(0, 0)
Sigma_beta_0_inv <- diag(2)
XSigX <- Reduce(
  `+`, lapply(X, function(X) t(X) %*% solve(Sigma) %*% X)
)
XSigU <- Reduce(
  `+`, mapply(function(X, U) t(X) %*% solve(Sigma) %*% U, X, U,
  SIMPLIFY = FALSE)
)
R <- 10
beta_draws <- replicate(
  R, update_coefficient(mu_beta_0, Sigma_beta_0_inv, XSigX, XSigU),
  simplify = TRUE
)
rowMeans(beta_draws)
#> [1] -0.8986910  0.9530168