Appendices to “To Center or Not to Center: That is Not the Question — An Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency”
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چکیده
p(ξt|ξt−1, ξt+1, β, ρ, δ, Y ) ∝ exp{−(ξt − μt) /(2σ t ) − dte tt}, where μt = (Ytδ 2 + (ξt−1 + ξt+1)ρ)/(1 + ρ ), σ t = δ /(1 + ρ), if t 6= 1 and t 6= T , and μ1 = Y1δ 2 + ξ2ρ, μT = YT δ 2 + ξT−1ρ, σ 2 1 = σ 2 T = δ . Define lt(ξt) = log p(ξt|ξt−1, ξt+1, β, ρ, δ, Y ). First, use Newton-Raphson to locate the mode x of lt and then calculate l ′′ t (x). Then draw t5 according to a t distribution with 5 degrees of freedom, and propose ξ t = x + t5/ √
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To Center or Not to Center: That Is Not the Question-An Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Efficiency
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