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