Table 3.
Comparison of effective sample size (ESS), effective samples per second(ES/sec), and relative speedup of ES/sec for φ, β, and w from Example 3. All algorithms were run for 120, 480 iterations, but the first 20, 480 were discarded to allow for sampler tuning. For brevity we provide only the average efficiency β̄ for the fixed effects β, and the average efficiency ω̄ for the spatial random effects w.
| φ | β̄ | ω̄ | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
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| Sampling Approach | Parallel API | ESS | ES/sec | ES/sec Speedup | ESS | ES/sec | ES/sec Speedup | ESS | ES/sec | ES/sec Speedup |
| φ, β, w | — | 1561 | 0.04 | 3614 | 0.08 | 2370 | 0.05 | |||
| OpenMP | 1548 | 0.05 | (1.46) | 3360 | 0.11 | (1.37) | 2364 | 0.08 | (1.47) | |
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| φ, β, {w} | — | 1564 | 0.03 | (0.88) | 5171 | 0.10 | (1.26) | 5587 | 0.11 | (2.07) |
| OpenMP | 1679 | 0.05 | (1.68) | 4246 | 0.13 | (1.62) | 6165 | 0.19 | (3.42) | |
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| φ, {β}, w | — | 1504 | 0.03 | (0.96) | 1316 | 0.03 | (0.36) | 2343 | 0.05 | (0.96) |
| OpenMP | 1484 | 0.05 | (1.36) | 2207 | 0.07 | (0.88) | 2403 | 0.08 | (1.45) | |
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| φ, {β, w} | — | 1673 | 0.03 | (0.94) | 35141 | 0.70 | (8.56) | 39424 | 0.79 | (14.64) |
| OpenMP | 1777 | 0.06 | (1.56) | 34706 | 1.08 | (13.11) | 38568 | 1.19 | (22.21) | |
Note that {θ1, θ2} denotes a joint update of parameters θ1 and θ2 using a factor slice sampler. The first sampling approach: “φ, β, w” employs standard univariate slice samplers for all parameters and was used as the baseline for determining the algorithmic speedups shown above.