Chapter 1. Stochastic simulation

· Example 1.2 (page 20) – Figure 1.1 (page 21) – Routines to sample from

(a) N(0,1) - central limit theorem applied to averages of uniforms

(b) N(0,1) - probability integral transform

(c) N(0,1) - Box-Muller algorithm

(d) N(0,1) - Modified Box-Muller algorithm

(e) Poisson

(f) Gamma(a,1) with a < 1

(g) Gamma(a,1) with a > 1

(h) Beta(a,b) with a,b<1

(i) Student’s t

· Figure1.2 (page 26) – Enveloping a normal density by a Cauchy density.

· Example 1.3 (page 27) – Figure 1.3 (page 27) – Rejection method: sampling N(0,1) draws from Cauchy(0,2.5) draws.

· Figure1.4 (page 32) – Inadequacy of the SIR method when the overlap between the proposal density and the target density is relatively small.