Algorithm 2: Univariate Factor Slice Sampling Update Algorithm for β ∈ ℝK with density proportional to f(β). Note: ηk ∈ ℝ1 is a parameter in the orthogonalized space. The basis vectors, Γk ∈ ℝK are chosen as eigenvectors of the covariance matrix of β.

1. Sample h(i) ∼ Uniform on {0, f(β(i−1))}

2. Set β(*) = β(i−1)

3. For each basis vector Γk ∈ Γ:

(a) Sample ${\eta }_k^{(i)}\sim \text{Uniform on}A=\{{\eta }_k:f({\eta }_k{\mathrm{\Gamma }}_k+{\mathit{\beta }}^{(\ast )})\ge h^{(i)}\}$

(b) Update ${\mathit{\beta }}^{(\ast )}={\mathit{\beta }}^{(\ast )}+{\eta }_k^{(i)}{\mathrm{\Gamma }}_k$

4. Set β(i) = β(*)