# MCMC (7) : Slice Sampling

Slice sampling algorithm A single transition $(x,u) \rightarrow (x',u')$ of a one-dimensional slice sampling algorithm has the following steps. (1). evaluate $P^* (x)$ (2). draw a vertical coordinate $u' \sim$ Uniform$(0,P^* (x))$ (3). create a horizontal interval $(x_l, x_r)$ enclosing $x$  3a. draw $r \sim$ Uniform$(0,1)$  3b. $x_l := x-rw$  3c. $x_r := x+(1-r)w$  3d. while $(P^* (x_l) > u')$ ${x_l := x-rw}$  3e. while $(P^* (x_r) > u')$ ${x_r:= x+w}$

#### Namshik Kim

physicist, data scientist

Data Scientist