Table 1 Scheme of ABC and required settings for simulation-based estimation
ABC steps | ||
|---|---|---|
1 | θ* ~ p(θ); generate θ* from prior distribution | |
2 | D* ~ f(θ*); generate pseudo data | |
3 | Compute summary statistics, S(D*), from D* and compare with given summary statistics, S(D). | |
If ρ(S(D*),S(D)) < ε, then θ* is accepted | ||
Repeat steps 1–3 many times to obtain enough number of accepted θ* for statistical inference | ||
Settings for simulation-based estimation of mean and standard deviation | ||
Specify | Example | |
A | Underlying data distribution. (e.g.: normal, log-normal, exponential) | Normal (μ, σ) |
Given the nature of the outcome variable, an educated decision about the underlying distribution can be made. | ||
B | Prior uniform distribution for each underlying parameter. | For μ, use U(Xmin, Xmax) in S1, or |
U(XQ1, XQ3) in S2 and S3. | ||
For σ, use U(0, L) where L denotes some large number beyond Xmaxin S1 or XQ3 in S2 and S3. | ||
C | Acceptance percentage and number of iterations | Acceptance of 0.1 % and 50,000 or 100, 000 iterations. |