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Non-informative prior for the linear model

Source: R/msm043.R
Msm043.Rd

Formula: f(beta, sigma2) proportional to sigma^-2 (eq. 6.2), flat in beta and in log(sigma). It is improper because it does not integrate to one, yet yields a proper posterior whenever X has full column rank. The density is returned up to its (infinite) normalizing constant.

Usage

Msm043(sigma2, beta = NULL)

Arguments

sigma2

Error variance, strictly positive.

beta

Regression coefficients; the prior is flat in beta so this is accepted for signature compatibility and does not enter the density.

Value

List with estimate, density, log_density, proper, method.

References

Montesinos Lopez, Montesinos Lopez & Crossa (2022), Multivariate Statistical Machine Learning Methods for Genomic Prediction, Springer, eq. (6.2) p.172. DOI 10.1007/978-3-030-89010-0.

Examples

# the improper prior p(beta, sigma2) proportional to 1 / sigma2
Msm043(sigma2 = c(0.5))$density
#> [1] 2