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Table 1 Scheme of ABC and required settings for simulation-based estimation

From: Simulation-based estimation of mean and standard deviation for meta-analysis via Approximate Bayesian Computation (ABC)

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.