TABLE 2:
Model parameters in the repressilator example. The second column presents the parameters of the prior distribution, where we use a Gaussian prior in the log10-transformed parameter space with a diagonal covariance matrix. The last four columns present the posterior mean and standard deviation of model parameters estimated using four methods: fixed-fidelity ST-MCMC (Fixed), Multifidelity ST-MCMC with ESS-Bridging, Multifidelity ST-MCMC with IT-Bridging, and Multifidelity ST-MCMC with β-tuning and IT-Bridging.
| Parameter | True | Prior | Posterior | |||
|---|---|---|---|---|---|---|
| Full-fidelity | ESS-Bridge | IT-Bridge | Tuned IT-Bridge | |||
| log10(k0) | 1.00 | 10.00 ± 0.3 | 1.00 ± 0.01 | 1.00 ± 0.02 | 0.99 ± 0.01 | 1.00 ± 0.01 |
| log1o(γ0) | −2.00 | 0.10 ± 0.3 | −1.98 ± 0.07 | −1.98 ± 0.08 | −1.98 ± 0.07 | −1.98 ± 0.07 |
| log10(a0) | −1.00 | 0.10 ± 0.3 | −1.05 ± 0.06 | −1.05 ± 0.07 | −1.07 ± 0.06 | −1.06 ± 0.06 |
| log10(b0) | 0.30 | 0.10 ± 0.3 | 0.31 ± 0.01 | 0.31 ± 0.01 | 0.31 ± 0.01 | 0.31 ± 0.01 |
| log10(k1) | 0.88 | 10.00 ± 0.3 | 0.87 ± 0.00 | 0.87 ± 0.01 | 0.87 ± 0.00 | 0.87 ± 0.00 |
| log1o(γ1) | −1.70 | 0.10 ± 0.3 | −1.71 ± 0.05 | −1.73 ± 0.06 | −1.73 ± 0.05 | −1.71 ± 0.05 |
| log10(a1) | −2.00 | 0.10 ± 0.3 | −1.98 ± 0.05 | −1.98 ± 0.06 | −1.99 ± 0.05 | −1.98 ± 0.05 |
| log10(b1) | 0.40 | 0.10 ± 0.3 | 0.40 ± 0.01 | 0.40 ± 0.01 | 0.40 ± 0.01 | 0.40 ± 0.01 |
| log10(k2) | 1.00 | 10.00 ± 0.3 | 0.98 ± 0.01 | 0.99 ± 0.01 | 0.98 ± 0.01 | 0.98 ± 0.01 |
| log10(γ2) | −1.30 | 0.10 ± 0.3 | −1.34 ± 0.03 | −1.34 ± 0.04 | −1.34 ± 0.03 | −1.34 ± 0.03 |
| log10 (a2) | −1.30 | 0.10 ± 0.3 | −1.35 ± 0.06 | −1.34 ± 0.07 | −1.36 ± 0.06 | −1.35 ± 0.06 |
| log10 (b2) | 0.48 | 0.10 ± 0.3 | 0.48 ± 0.01 | 0.48 ± 0.01 | 0.48 ± 0.01 | 0.48 ± 0.01 |