Table 1.
|
Simulation 1 |
Simulation 2 |
Simulation 3 |
|||
---|---|---|---|---|---|---|
MA | MAP | MA | MAP | MA | MAP | |
BVS: EB prior† |
0.819±0.004 |
0.850±0.004 |
0.837±0.004 |
0.889±0.005 |
0.899±0.002 |
0.918±0.002 |
BVS: flat prior† |
0.845±0.004 |
0.919±0.005 |
0.845±0.004 |
0.919±0.006 |
0.904±0.002 |
0.927±0.003 |
BVS: ‘incorrect’ prior† |
0.858±0.003 |
0.895±0.003 |
0.918±0.003 |
1.003±0.004 |
0.969±0.003 |
1.036±0.003 |
BVS: MRF prior† |
0.830±0.004 |
0.877±0.005 |
0.871±0.004 |
0.920±0.006 |
0.886±0.002 |
0.911±0.002 |
Lasso† |
0.791±0.003 |
0.790±0.003 |
0.913±0.002 |
|||
Li&Li |
1.246±0.009 |
1.476±0.012 |
1.760±0.012 |
|||
Baseline linear | 1.000±0.002 | 1.000±0.002 | 1.000±0.002 |
Predictions using small-sample training data (n = 35) and held-out test data (n = 818; total of 5,000 train/test pairs) for Simulations 1, 2 and 3. Results shown are mean absolute predictive errors ± SEM for the following methods: Bayesian variable selection (BVS) with biologically informative pathway-based prior with source and strength parameters set by empirical Bayes, BVS with flat prior, BVS with ‘incorrect’ prior (contradicting empirical Bayes; see text for details), BVS with a Markov random field (MRF) prior, Lasso regression, penalised-likelihood approach proposed by Li and Li [21], and a baseline linear regression without interaction terms including all 11 predictors. For BVS, predictions made using the posterior predictive distribution with exact model averaging (‘MA’) and using the maximum a posteriori model (‘MAP’).
‡ linear model with interaction terms for Simulations 1 and 2, and without interaction terms for Simulation 3.