Suitable uses

Ratio-of-Uniforms is a rejection sampling method. Its speed is linear in the probability of acceptance \(p_a\). When \(p_a\) is low, say \(p_a < 0.01\), the sampling is slow. In particular, the higher the dimension, the smaller \(p_a\) gets.

Ratio-of-Uniforms does not work for all probability densities. It is required of \(f(x_1, ..., x_d) \), that

• \(f\) is bounded
• \(x_i f(x_1, ..., x_d) ^ \frac{r}{1+rd}\) is bounded for \(i = 1..d\), where \(r\) is a tuning parameter that is by default set to 0.5.

Many commonly used distributions have no problems.

For a more detailed discussion referring to the R package RUST, refer to When can rust be used? by Paul Northrop.