Table 2.
ESS for log posterior density, ρ and median (range) of 200 sample function values by dataset for three sampling approaches: 1.) sampling γ and ρ using simple Metropolis-Hastings, 2.) jointly sampling each of σ2 and ρ with u based on conditional Gibbs sample for u, and 3.) jointly sampling each of σ2 and ρ with u and λ as in (19-20). η2 is fixed at 0.32. ’NM’ indicates that the chain has not burned in or is mixing so slowly as to make calculation of ESS uninformative.
| Sampling Method | ||||
|---|---|---|---|---|
| Quantity | Dataset | simple: γ,ρ | joint, Gibbs: σ2,ρ | joint, deterministic: σ2,ρ |
| Data1 | NM | 42 | 193 | |
| LP | Data2 | NM | 87 | 205 |
| Data3 | NM | 17 | 447 | |
| Data5 | NM | 143 | 646 | |
| Data1 | NM | 37 | 146 | |
| ρ | Data2 | NM | 70 | 145 |
| Data3 | NM | 15 | 414 | |
| Data5 | NM | 125 | 289 | |
| Data1 | 549 (28-1898) | 510 (34-1338) | 597 (90-1808) | |
| f | Data2 | 1806 (22-3496) | 1805 (132-3763) | 2137 (229-4231) |
| Data3 | 236 (5-2154) | 611 (200-3062) | 657 (307-3232) | |
| Data5 | 1563 (17-6503) | 1964 (519-8958) | 2021 (467-8971) | |