Sample the linear regression parameters assuming a g-prior

Sample the parameters for a linear regression model assuming a g-prior for the coefficients.

Usage

sample_lm_gprior(y, X, params, psi = NULL, XtX = NULL, X_test = NULL)

Arguments

y

n x 1 vector of data

X

n x p matrix of predictors

params

the named list of parameters containing

1. mu: vector of conditional means (fitted values)

2. sigma: the conditional standard deviation

3. coefficients: a named list of parameters that determine mu

psi

the prior variance for the g-prior

XtX

the p x p matrix of crossprod(X) (one-time cost); if NULL, compute within the function

X_test

matrix of predictors at test points (default is NULL)

Value

The updated named list params with draws from the full conditional distributions of sigma and coefficients (along with updated mu and mu_test if applicable).

Note

The parameters in coefficients are:

• beta: the p x 1 vector of regression coefficients components of beta

Examples

# Simulate data for illustration:
sim_dat = simulate_nb_lm(n = 100, p = 5)
y = sim_dat$y; X = sim_dat$X
# Initialize:
params = init_lm_gprior(y = y, X = X)
# Sample:
params = sample_lm_gprior(y = y, X = X, params = params)
names(params)
#> [1] "mu"           "sigma"        "coefficients"
names(params$coefficients)
#> [1] "beta"