In rdinnager/phurl: Phylogenetic modelling Using Regularized Linear models

knitr::opts_chunk$set(echo = TRUE)

Bayesian Ridge Regression Equations

The Bayesian version of Ridge regression treats the \eqn{\beta} coefficients as being drawn from a gaussian distribution with mean 0 and a shared standard deviation. This standard deviation parameter itself has an inverse gamma prior distribution. This has the effect of "shrinking" coefficients towards zero where the strength of this shrinkage is inversely proportional to the gaussian standard deviation. E.g.: $$y_i \sim f\left(\mu_i, \phi\right)$$

$$g\left(\mu\right) = \alpha + \sum_j\beta_jx_i$$ $$\beta_j \sim \text{Normal}\left(0, \tau\right)$$

$$\tau \sim \text{InvGamma}\left(1, 1\right)$$

https://arthursonzogni.com/Diagon/#code_area

y_i = f(μ, φ)

       ===       
       \

g(μ) = α + / beta_j ===
j

beta_j = Normal(0, τ)

τ = InvGamma(1, 1)

rdinnager/phurl documentation built on Dec. 8, 2019, 3:06 p.m.