Chapter 3. Approximate methods of inference

· Example 3.1 (pages 84) – Figure 3.1 (page 85) - Poisson data (one single observation) with conjugate Gamma prior.

Figure 3.1 exhibits exact posterior density (Gamma) as well as a normal approximation and two non-normal approximations.

· Figure 3.2 (page 101) – Bayes’ theorem via the rejection method in the context of Example 2.1 and Figure 2.1.

· Example 3.6 (pages 102) – Figure 3.3 (page 103) - Weighted resampling algorithm (SIR) to simulate from

π(θ) ∝(2+θ)¹²⁵(1-θ)³⁸θ³⁴

for θ in [0,1].

· Example 3.7 (pages 102-3) – Figure 3.4 (page 104) - Weighted resampling algorithm (SIR) to simulate from

π(β) ∝ (∑[y_i-β₁-β₁e^-β₂x_i]²)^-2

for β=(β₁,β₂) in [-20,50]x[-2,6] , x = (1,2,3,4,5,7) and y = (8.3,10.3,19,16,15.6,19.8).

· Example 3.8 (pages 106-7) – Figure 3.5 (page 107) - Bootstrap filter applied to the first order dynamic linear model of Example 2.9 (pages 63-4).