Table 3.
Illustrative computation times
| |
Linear model without interaction terms |
|
Linear model with interaction terms |
||||||
|---|---|---|---|---|---|---|---|---|---|
| dmax = 2 | dmax = 3 | dmax = 4 | dmax = 5 | dmax = 2 | dmax = 3 | dmax = 4 | dmax = 5 | ||
| p=30 |
0.1 |
1.1 |
8.7 |
9.5 |
|
0.4 |
4.7 |
38.6 |
374.6 |
| p=60 |
0.5 |
10.5 |
114.3 |
− |
|
1.8 |
39.4 |
661.6 |
− |
| p=120 |
2.8 |
116.3 |
− |
− |
|
8.2 |
350.1 |
− |
− |
| p=500 | 150.3 | − | − | − | 238.7 | − | − | − | |
Computation times (in seconds) for proposed Bayesian variable selection procedure, using empirical Bayes to select between two priors (M = 2) and to set the prior strength parameter λ (optimisation performed over ten values of λ). Results shown for varying values of dmax (maximum number of predictors allowed in a model) and p (total number of predictors), for both a linear model without interaction terms and a linear model with interaction terms. (Data and model priors generated using random numbers and results are averages over three iterations. Computation performed on a standard single-core personal computer; 1.6GHz, 2GB RAM. ‘-’ denotes a (p,dmax) regime where the procedure failed due to insufficient memory).